Cool rumor du jour: Viggo Mortensen may be up for the role!
(To debut in the next Thor movie, then presumably move on to his own solo movie.)
Let's see, right looks, talented, and the right age. Viggo would ensure they don't make the mistake of casting the role too young. Dr. Strange has white in his hair and a successful medical career in his backstory. It would make sense for him to be at least 40 when his story began.