The two names that keep floating in my head as feeling right for AVP movie are Dan Trachtenberg and David Twohy (Twohy being a name I'd also be very happy to see attached to a standalone Predator movie). Maybe André Øvredal...
Were it not for the stories about Alex Garland ghost directing the film, I'd have said Pete Travis based on
Dredd – but Garland is someone that I think would be a very good fit for an Alien movie proper, not AVP.
Were it not for the "Alien 5" fiasco, Neill Blomkamp is probably another one I theoretically might have said, at some point in the past, would have the right sensibilities for an AVP. It'd never happen now though, and that's fine.
Oh, you know what, I'm also going to throw Robert Rodriguez's name out there, if he were to actually personally direct it and not feel like he was falling asleep halfway through writing the shooting draft of the script (*cough*
Predators *cough*). Get him on some of that
Alita: Battle Angel juice, mix in some
From Dusk Till Dawn/
Planet Terror, and let him have at it, even if he does insist in shooting in his backyard in Texas.