Poythress averaged 11.2 points and six rebounds per game this season for the Wildcats and some scouts saw him as a first-round selection in June's NBA Draft had he chose to leave school.
The Wildcats went 21-12 this season missing the NCAA Tournament a year after winning the national title. They lost in the first round of the NIT to Robert Morris.
"This year didn't end like we wanted it to," Poythress said. "I want to come back and do what we said we wanted to do and that's win a national title. I want to develop more as a player and the competition coming in next year should help me do that.