The film, "The Social Network," is scheduled to be shown as part of the New York Film Festival next month.
The Times said Facebook founder Mark Zuckerberg and other Facebook insiders are in a tense standoff with the filmmakers, who portray the the creation of Facebook as a serials of betrayals fueled by computer users who have an insatiable desire for "friends," which is what the site calls participants.
Privately, Zuckerberg, a 26-year-old billionaire, says the film is not true, the Times said.
Chris Hughes, a Facebook co-founder who left in 2007 for the Obama campaign, agrees.
"It's crazy because all of a sudden Mark becomes this person who created Facebook to get girls or to gain power," Hughes said. "That's not what was going on. It was a little more boring and quotidian than that."
One of the film's producers, Scott Rudin, said two top Facebook executives "saw the movie a while ago, and they do not like it." Rudin said filmmakers tried to make small changes to ease tensions, but declined to make big changes demanded by Facebook, headquartered in Palo Alto, Calif.