According to an interview with Zap2it, the director Seth Gordon (Horrible Bosses, Identity Thief) confirmed that the Uncharted movie will start filming in early 2015.
In response to a question about when they'll begin shooting, Gordon said, "I think very early next year. That's the plan. That's like tomorrow, essentially, because the prep is so complicated for the movie."
Even if the movie production is about to begin early next year, Gordon said he has no idea about the actor who will play Nathan Drake in the movie:
"I want it to be a great actor," he said. "That's number one, and then if it's someone who has an actual jaw, that's even better. The game is so well done that you need it to live up to that. There's no way we'd do the inverse of that where it's somebody famous who can't [act]."
In the previous attempt, when David O. Russell was set to direct that movie, the actor named for that role was Mark Wahlberg (Transformers 4: The Age of Extinxtion), but it's not clear if he might once again be called upon.