CAD mocked the Statham-as-Doctor idea
in one of the comic's rare funny strips. I've not seen Looper
yet or read reviews, but based on the trailer it looked very much like what I think a high-octane action timey-wimey Doctor Who
I wouldn't object to Statham as the Doctor.
For a more realistic choice, I'd like to see James Frain as the 12th Doctor.