The Canaries and Birmingham are said to be keen on the 24-year-old Israeli, says Sky Sports News.
Abada currently plays for Charlotte FC – managed by former Norwich boss Dean Smith – in the MLS.
The Championship rivals are not alone, with a number of clubs said to be interested.
Abada’s current contract runs until the end of 2026, with Charlotte having an option to extend it by a year.
Abada has scored 13 goals in 76 appearances since leaving Celtic in 2024 for a reported £8m fee.
It was claimed at the time he had faced pressure from compatriots to leave Celtic after some fans showed their support for Palestinian people.
“After two and half incredible years, the time has come to bid farewell,” he said. “The past six months have been a personal challenge, yet the overwhelming support from the gaffer, coaches and board has been my rock. Their unwavering faith during these times won’t be forgotten but cherished forever.”
Abada joined Celtic in July 2021 from Maccabi Petah Tikva and was a key player under Ange Postecoglou.
Smith was delighted to have captured Abada for Charlotte.
“He’s a player that I know well coming from the UK,” he said at the time. “I know he’s been playing in Scotland, but there are not many English people who don’t know about Celtic and Rangers players because they’re always in the news and they’re on the TV a lot.
“They’re both two big clubs and to get a player of his calibre and the consistency he’s had in the last couple of seasons with Celtic is a big coup for ourselves, I believe.
“He’ll add creativity in the final third. He scores goals and he creates goals. I think the last two seasons he’s probably scored 10 and created seven or eight. If you’re getting a player, a wide player that’s having 18 goal involvements a season, then that’s a good player.
“We believe that Liel Abada will be the right player and the right person with the right character.”