Burger took charge when David O Russell left the project over "creative differences" with the studio.
He told Collider: "We're rewriting it and I'm just jumping in right now to do it. The deal really has just closed, so it's very, very new. I'm basically writing it from scratch.
"So, it's a ways off, but it's very exciting to have something that could be a franchise. I like it, and I like that it's a bit different from a lot of the science fiction stuff that's out there. I like that it's a classic, great adventure."
Uncharted: Drake's Fortune sees players following Drake as he seeks out lost gold thought to be located in the mythical land of El Dorado.
Burger added that there is nothing wrong with using video games for inspiration.
"I pitched [the studio] something that was very true to the video game, but that just makes it into a movie that supports what's best about the video game, and I think that they dug that," the director said.
"I just think you have to make the best movie you can. Something like Indiana Jones was updating 1930s B-movies.
"In the same way, we're inspired by the video game, but we have to do what a movie does best."
It is not known whether Mark Wahlberg will stay on for the adaptation after the departure of The Fighter helmer Russell.
Watch the trailer for Neil Burger's Limitless below: