Travolta had been attached to play J.R. Ewing in the big-screen version of "Dallas" for more than two years.
But the New York Post's Page Six column quoted an insider who said Travolta was "let go about two weeks ago. He had the role of J.R. Ewing taken from him and given to Ben Stiller."
Initially intended as a big-screen drama, the film is reportedly now being conceived as a comedy with a scaled-back budget.
"John was given a nice seven-figure 'gift' to go away quietly," the source told the Post. "He also got five family members roles in the movie and they aren't going to be in it now, either."
Although a representative for Travolta declined to comment, a friend told Page Six: "He is not doing the movie. They've gone in a different direction than was originally intended. I don't know about any 'gift' and I don't think the family member thing is correct."
A representative for Stiller denied he has accepted or even been offered the role.