The actor is also eyeing a deal to produce the potential series, which is backed by Fringe producers Roberto Orci and Alex Kurtzman's KO Paper Products, reports Deadline.
The show centres on five experts commissioned by the CIA to help extract an agent from a mission when things go bad.
Hawke would play the leader of the team of experts in the globetrotting series that would see the show moving to different countries every week.
The show would also use the real-time storytelling device used in Fox's 24.
The project would mark Oscar nominee Hawke's first regular TV series gig.