Citing emails between Sony studio executives that were leaked by hackers last year, the Times said marketing plans for the movie were positioned to focus on the story of a whistle-blower, rather than a condemnation of the sport.
Sony said on Wednesday that the New York Times story "contains many misleading references" and that nothing had been "softened" in the film to placate anyone.
The movie, starring Will Smith as a pathologist who diagnosed a degenerative brain disease in U.S. football players, is due in movie theaters in December. A first trailer was released on Monday, and the movie is seen as a potential Oscar contender.
The NFL in April settled a lawsuit brought by about 5,000 former players who accused it of covering up the dangers of concussions.
"Will (Smith) is not anti football (nor is the movie) and isn’t planning to be a spokesman for what football should be or shouldn’t be," Dwight Caines, the president of domestic marketing at Sony Pictures, wrote in an email on Aug. 6, 2014, to three top studio executives about how to position the movie, according to the New York Times report.
"We’ll develop messaging ... to ensure that we are telling a dramatic story and not kicking the hornet’s nest," it quoted the email as saying.
Another 2014 email quoted by the Times said some "unflattering moments for the NFL" were deleted or changed, while another note said a top Sony lawyer had taken "most of the bite" out of the film.
Sony said the Times article and headline had been written "by individuals who have not seen the film (and) contains many misleading references."
"As will become immediately clear to anyone actually seeing the movie, nothing with regard to this important story has been 'softened' to placate anyone," Sony Pictures Entertainment spokeswoman Jean Guerin said in a statement.
The NFL declined to comment on the report but said in a statement it was encouraged by the focus on player health and safety.
"We all know more about this issue than we did 10 or 20 years ago. As we continue to learn more, we apply those learnings to make our game and players safer," it said.