NEW YORK — Before and after every practice at the MSG Training Center, New York Rangers defenseman Braden Schneider walks past a Wayne Gretzky quote displayed in the hallway leading from the ice to the locker room.

It reads: “The greatest place to play as a professional athlete is right here in New York.”

Seeing it makes Schneider think back to his first three seasons, two of which ended with trips to the Eastern Conference Final. That was his introduction to the thrill of playing at Madison Square Garden.

“It’s everything,” Schneider told The Athletic earlier this week. “The memories of having that building rocking early on and going deep in playoffs, that’s the feeling that you work for.”

Now in his fifth season, Schneider is experiencing a much different atmosphere at MSG. Thursday’s 3-2 overtime loss to the Philadelphia Flyers dropped the Rangers to 6-15-5 on home ice and 22-29-7 overall as they head toward a second straight season with no playoffs.

It’s been a jarring turn of events for a 24-year-old who’s realizing that NHL wins aren’t as easy to come by as it initially appeared.

“With the success that we had, I think maybe you started expecting a little bit more than you should,” Schneider said. “Not that we don’t work hard or do all that. We compete and we know how to push each other, but I think it’s been humbling, for sure. That kind of goes back to me saying there’s lots of lessons and things to be learned throughout this season that we’re having. I think that’s the best way to look at it, because you go from winning early, and then it seems harder, almost. It’s definitely a mental battle. I know everyone in here feels that.”

The losing has forced Schneider to come to grips with an uncertain future. In the aftermath of team president Chris Drury’s Jan. 16 retool letter, the Rangers have been fielding calls and gauging the market for him.

Drury has set a high asking price, with teams being told he’s content to hold the 6-foot-3, right-shot defenseman if no one meets it, according to two league sources. His preference is a hockey trade, meaning a return centered around young players who are ready to contribute, rather than draft picks and future assets. The belief is an impact forward would have to be included to convince New York to part with a high-character player who remains well-thought-of throughout the organization.

Schneider is still young enough to be part of the solution, but he’s blocked on the right side by Adam Fox and Will Borgen, who are both under contract until at least 2029. The Rangers shifted him to the left side for Thursday’s game in an effort to expand his role, with head coach Mike Sullivan saying, “What I admire about Schneids is he’s willing to embrace anything we ask of him.” But if they can trade from an area of strength to address a position of need — of which they have many — Drury will have to consider it.

“You don’t want to be on that side of things,” Schneider said of the trade rumors. “You want to be on the team that’s adding and you’re keeping your group intact. We all care for each other like family in this room, and when it comes to that, it sucks. But at the end of the day, we’re struggling, and it seems like you’ve got to be ready for change.”

“I’ve been a guy that’s been thrown around out there,” he added. “It’s hard to accept, because you look back on the year and you wish you could have done more and helped your team win more games. But at the end of the day, that’s the NHL, and that’s the business of it.”

The Rangers must also consider Schneider’s career trajectory. He was averaging a career-high 20:19 time on ice per game entering Thursday, but his game hasn’t taken off with the added minutes. He’s trending toward his lowest point total since his rookie season, with only 11 (two goals and nine assists) through 58 games, and has posted a 43.68 percent expected goals-for rate that ranks last among the team’s defensemen, according to Natural Stat Trick.

“With the puck we definitely needed to bear down a bit more, and I feel like that goes especially for me,” Schneider said. “There have been opportunities to capitalize here and there. And then on the other side defensively, you want to be a positive player — plus-minus and on the ice for more goals. It’s just been a hard year.”

Schneider’s future with the Rangers remains uncertain. (Dennis Schneidler / Imagn Images)

The team context matters, with the Rangers as a whole struggling mightily for most of the season. But if they’ve determined Schneider’s ceiling is limited and find a trade partner coveting big, physical defensemen who makes a significant offer, they may want to capitalize before that value diminishes.

There’s a chance that happens before next Friday’s 3 p.m. trade deadline, but I don’t sense anything is imminent. Schneider will be a restricted free agent this summer, at which point Drury could reevaluate and circle back on some of the trade discussions that have begun in the last numbers of weeks.

“No matter what happens, I’ll always feel grateful to have been a Ranger,” said Schneider, who quickly corrected himself: “To be a Ranger.”

The latest on Trocheck

While Schneider being traded feels like a 50-50 proposition, the perception around the league is that Vincent Trocheck is the likeliest Ranger to be dealt in the next week. The Minnesota Wild are considered the favorite by just about everyone I’ve talked to — a rumor Trocheck himself acknowledged during a lighthearted scene at the Olympics — but with the moment of truth approaching, I’m sensing a hint of skepticism.

Colleague Michael Russo, who does a wonderful job covering the Wild, came on “The Flying V” podcast this week and reiterated that Minnesota is among the interested parties. But he also raised a legitimate question about whether Wild general manager Bill Guerin is willing to part with the necessary assets to get it done, particularly after sacrificing such a significant haul to acquire Quinn Hughes in December. Russo believes 2022 first-rounder Danila Yurov, who our prospects writer Corey Pronman ranks as Minnesota’s top under-23 player, would be very difficult to pry away.

I’ve heard the same, which is why in my Jan. 28 insider column I wondered about a package headlined by the Wild’s No. 2 prospect Charlie Stramel, plus a young defenseman such as David Jiříček or Carson Lambos and a future first-round pick. But is that enough to get Drury to say yes? Stramel is having a breakout season for Michigan State and ranks 12th in the NCAA in scoring with 40 points (19 goals and 21 assists) through 30 games, but he’s considered a likely middle-six center at the pro level.

Just because Drury and Guerin joined forces to help Team USA win gold in Milan doesn’t mean he owes his American counterpart any favors. Drury can’t afford to take anything less than the best available deal, especially after being backed into a corner by Artemi Panarin and his no-movement clause earlier this month.

Whether there’s a team out there that’s willing to offer more than Minnesota is a point of major curiosity. We’ve previously connected the Carolina Hurricanes and Detroit Red Wings to Trocheck, but are either of those general managers prepared to trade away their top assets? Detroit’s Steve Yzerman, in particular, has a reputation for clinging tightly to his.

A team that seems motivated to make a splash is the Utah Mammoth, but the belief is that Trocheck prefers to stay east, raising questions about whether he has them on his 12-team no-trade list. Would he make an exception for established contenders such as the Colorado Avalanche or Dallas Stars? Both are tight on salary cap space, but the Avs freed some up Tuesday by sending defenseman Samuel Girard to the Pittsburgh Penguins.

I’m sure there’s a mystery team involved, as well. (Boston? Buffalo? L.A.?) The more the merrier for Drury, who has seven days left to drive up the price on the No. 1 player on Chris Johnston’s trade board.

Could the Rangers take the position that they don’t have to trade Trocheck now? He has three remaining years on his contract at a manageable $5.625 million average annual value, giving them the option to kick the can down the road. They’re surely using that as a negotiating tool, but the iron may never be this hot again. Trocheck is coming off a strong showing at the Olympics and stands as arguably the best center available in a market that’s light on options at that premium position. He’ll turn 33 this summer, with his value likely to decrease as he gets older.

I’m still betting a trade gets done by next Friday, and it’s entirely possible that the Wild are the last team standing, as we’ve suspected all along. This is smokescreen season after all, with teams maneuvering to mask their intentions as the deadline approaches. But at least at this hour, my impression is that the Rangers are continuing to shop around with the hope of convincing a suitor to raise the stakes.

Fox, Shesterkin address the retool

I’ve been told none of the remaining Rangers with no-movement clauses — Adam Fox, Vladislav Gavrikov, J.T. Miller, Igor Shesterkin and Mika Zibanejad — will be moved before the deadline, but it’s possible further discussions about their futures in New York occur during the offseason.

Fox and Shesterkin returned to the lineup Thursday after missing the previous 13 games due to lower-body injuries sustained on Jan. 5. Neither had spoken since Drury’s letter, with both asked for their reactions after the game.

“I don’t care about that letter and all this stuff around,” Shesterkin said. “I need to do my job. I need to stop the puck. I need to give a chance to my teammates to get two points every night.”

When asked if he plans to stick around through the retool, the 30-year-old goalie simply said, “I just do my best, and I hope everyone tries (to do) the same.”

Fox echoed those sentiments and was notably noncommittal about anything beyond this season.

“I’m just trying to focus on this year right now and play each game,” he said. “That’s really all I can do right now, can control. I was just trying to work to get back and help the team finish strong. That’s where my head’s at, obviously. That’s the focus right now. I think that’s a conversation when we’re done playing.”