"There's no question in my mind that he is definitely equipped and ready to be paid," Self said Tuesday. "No question. Now, the question to the family is, 'Is he ready to play and impact the NBA game?'
"I personally think he can do that. But that's something they need to decide as a group."
The 6-6 guard averaged 13.4 points for the Jayhawks, who were ousted in the second round of the NCAA tournament.
Self also said he expected junior center Cole Aldrich to decide in about a week whether he will enter the NBA draft or remain for his senior season.
"I'll meet with X and see what he and his family want me to do," Self said. "I'll do whatever they want me to do, but that will be a family decision. There is no timetable I have whatsoever on them getting together and making a decision. I don't think a decision has been made yet. I think there's probably a way in which they're leaning. But we'll wait and see what happens.
"With Xavier, we knew there would be a great chance he would be one-and-done. I'll support whatever direction they go."
Self said he visited with Aldrich on Monday. The 6-11 center averaged a shade less than a double-double and set the school record for blocked shots in a season.
"To me, with Cole, it doesn't have much to do with where people have him projected [in the draft]. We know he's going to get drafted pretty high," Self said. "It's what would be best for his family. It could be best for his family for Cole to come back. But I've said this all along, I'm not encouraging that at all. I think it's something he has to feel totally comfortable with."