Hollywood super producer Ryan Murphy is being dubbed “insensitive” for failing to push back his new Kennedy drama in the wake of Tatiana Schlossberg’s death, a source told Page Six.

“American Love Story” — which focuses on the marriage and tragic deaths of John F. Kennedy Jr. and his wife, Carolyn Bessette-Kennedy — is slated to debut next month on FX and Hulu, just weeks after the December 30 passing of JFK Jr.’s niece Tatiana, 35, from leukemia.

A source who knows the Kennedy family told Page Six that the prospect of the drama airing as Caroline Kennedy, Tatiana’s mother and JFK Jr.’s only sibling, is “insensitive … this is a very sorrowful time for Caroline and for everybody in the family right now.”

Paul Anthony Kelly and Sarah Pidgeon play John F. Kennedy Jr. and Carolyn Bessette Kennedy in the new FX and Hulu series “American Love Story” — which is set to debut in February. A source said the show, which the Kennedy family opposes, will add to Caroline Kennedy’s stress as she is grieving the death of daughter Tatiana Schlossberg. BACKGRID

The real-life JFK Jr. and Carolyn Bessete-Kennedy were never out of the headlines during their torrid three-year marriage. Sygma via Getty Images

Some members of the family “assumed that the show would be pushed back, but there hasn’t been any mention of that,” the source said, adding that Caroline, 68, is way too dignified to even think of approaching the producers.

FX reps could not be reached for comment.

Tatiana’s brother, Jack Schlossberg, is one of the project’s biggest critics and previously slammed Murphy for creating the show about his late uncle without consulting the Kennedy family.

Tatiana Schlossberg is pictured with her husband, Dr George Moran, and their children, Josephine and Edwin, weeks before her death from leukemia aged 35. jfklibraryfdn/Instagram

Grieving Caroline Kennedy was seen holding her granddaughter, Josephine Moran, at her daughter Tatiana’s funeral on Monday in NYC. TheImageDirect.com

“For those wondering whether his family was ever consulted, or has anything to do with, the new shows being made about him, the answer is no,” Schlossberg, who is running for a US House seat in New York’s 12th congressional district, posted on Instagram in June. “For the record, I think admiration for my Uncle John is great. What I don’t think is great is profiting off of it in a grotesque way.”

Murphy bought the rights to Elizabeth Beller’s book, “Once Upon a Time: The Captivating Life of Carolyn Bessette-Kennedy,” to use as source material for the show, Beller’s publisher confirmed.

Schlossberg also criticized Murphy for not setting aside profits from the show for the Kennedy Library.

JFK Jr. and his wife died in a July 1999 plane crash alongside Carolyn’s sister, Lauren Bessette.

Ryan Murphy is the producer being “American Love Story” — and now being called “insensitive” by a Kennedy family source over the timing of the series. WireImage

Jack Schlossberg — seen with father Edwin Schlossberg at his sister Tatiana’s funeral — has lashed out at Murphy, calling “American Love Story” “grotesque.” Elder Ordonez/INSTARimages

After Schlossberg aired his grievances on social media, Murphy responded on the “This Is Gavin Newsom Podcast” that he “thought it was an odd choice to be mad about your relative that you really don’t remember.”

Schlossberg, who was 6 years old when his uncle died, shot back: “My earliest memories are of John calling me Jackolantern and ‘the nudist,’ picking me up from school, his Pontiac convertible. I remember being the ring bearer at his wedding and the day he died. I remember Wyclef singing at his funeral.”

He also claimed that Murphy is “making millions” off JFK Jr.’s life without contributing “any of your riches to the causes he championed, or the legacy of public service he represented.”

Paul Anthony Kelly, whose sole prior credit is a 2010 television series titled “Body Language,” plays JFK Jr. while Carolyn Bessette-Kennedy is portrayed by Sarah Pidgeon. Naomi Watts plays Jackie Kennedy and Grace Gummer portrays Caroline Kennedy.

Grace Gummer plays Caroline Kennedy alongside Paul Anthony Kelly as JFK Jr. in “American Love Story.” GC Images

Jack Schlossberg — seen here (right) with father Edwin, mother Caroline and sister Tatiana — blasted Murphy for claiming he did not even know his late uncle. AP

Tatiana, who penned an essay about her illness published by the New Yorker in November, left behind a 3-year-old son, Edwin, and 1-year-old daughter, Josephine, with her husband George Moran.

The Kennedy family was joined by former president Joe Biden and former New York City mayor Mike Bloomberg at Tatiana’s funeral service Monday.