The final chapter of Nathan Drake's story released earlier this year in Uncharted 4: A Theif's End as a PS4 exclusive. The definitive end for Nathan Drake's story accompanied with developers' decisive "no" to further sequels seems to have risen the previously rumored film from years in development hell.
Stranger Things' director Shawn Levi has taken lead on this project as director and has reportedly had several conversations with candidates for Nathan Drake. Joe Carnahan (The A-Team, The Grey) is attached as the lead writer, hoping to make Nathan Drake the anti-Indiana Jones-- an anti-hero-- emphasizing Drake's orphan backstory and thieving morality.
The goal is to have the film reach broad audiences, not just fans of the series. It's very clear that he is a fan of the series and knows the negative reputation that game-based movies receive, so there are high hopes with Carnahan's efforts in speaking to Amy Henning (director for Uncharted), and Nolan North (voice actor for Nathan Drake).
Previous names attached to the project such as Mark Wahlberg have dropped out, and Carnahan has dismissed the fan-favorite Nathan Fillion.
We will have more information as it is released.