Writer Neil Druckmann and producer Sam Raimi confirmed during a surprise Comic-Con panel that they have had a meeting with 17-year-old Williams, but nothing has yet been signed, reported E! online.
"I think it's going to be a great character journey and a great love story, and a great horror picture," said Raimi of the video game adaptation.
Druckmann said that his priority in working on the script was to "laser-focus" on the central relationship between Ellie and Joel, who are two survivors in a post-apocalyptic United States.
The acclaimed 2013 game follows the pair as they work together to survive their cross-country journey in search of a cure for the plague that has all but destroyed the human race.
"There's never been a really great movie made from a video game," Druckmann said.
"There have been ones that we've enjoyed but we thought, 'What if we could make the first great one' We're gonna work our asses off to make that happen."
A director for 'The Last of Us' is yet to be announced.