I have no clue whom he has chosen. My belief is he made the decision a while back, and is waiting to reveal it at a time when it will have the greatest strategic value.
There are two paths he can take, one, he pick a person who would seamlessly fill his shoes should something happen to him. Something like a Truman, a Johnson, either one would be unbearable.
The second type is the Gaffer Joe selection, some one so inept and stupid that no one, not even Kim Jong Un would want to kill him.
The revelation will come, and it will happen at a point in time where it will steal the press cycle for at least a day. Expect it to rob HiLIARy of her thunder at some near point.