David Twohy, despite his connection to Alien via his stab at Alien 3 pre-Fincher, strikes me as a guy that I'd really love to get a Predator movie out of, especially after really nailing that sort of pulpy tone in the 2013 Riddick.
AVP could also work from him, for sure, but something about Predator specifically seems like it'd be just the right fit for him.