The Abraham Lincoln: Vampire Hunter filmmaker will helm the project based on a screenplay drafted by F Scott Frazier, according to The Hollywood Reporter.
Heatseekers, originally scripted by George Mahaffey, follows an ex-military pilot who goes up against a group of sky pirates. Casting details are yet to be announced.
Bekmambetov, whose previous films include Night Watch and Day Watch, is also said to be working on a sequel to Wanted with James McAvoy attached to reprise his role from the original.
The Russian filmmaker turned down the opportunity to direct dark fairy tale The Last Witch Hunter - to which Vin Diesel is attached - last year in favour of helming Abraham Lincoln: Vampire Hunter.
Heatseekers is yet to be assigned a release date.
Watch a clip from Abraham Lincoln: Vampire Hunter below: