He's going to remain steadfast in his determination to simply ensure a nominee who holds the greatest promise of filling the very large shoes of the man who has just passed. I don't think he'll confine himself to any candidate of a particular race or gender.
The chief justice for 33 years has been the personification of the value of judicial restraint, and that is something that the president is equally committed to. I'm certain the president will abide by those beliefs as he looks for a nominee to replace him.