Cronin, 47, has steered the Bearcats for 13 seasons since leaving Murray State in 2006. He and Babcock have already worked with each other because Babcock used to be Cincinnati's athletic director.
Cronin, who was named the 2018 national coach of the year by The Sporting News, has won 296 games with the Bearcats. He led Murray State to 69 wins and two NCAA bids in three years before taking the Cincinnati job.
Cincinnati was ranked No. 24 in the final Associated Press Top 25 poll two weeks ago. The 28-7 Bearcats won the American Athletic Conference tournament for the second straight year.
The Bearcats lost to Iowa in the first round of this year's NCAA Tournament. They have made the NCAAs for nine straight years but have not reached the Sweet 16 since 2012. If Cronin feels Cincinnati fans are growing tired of losing in the first or second round, perhaps he would finally be interested in leaving his alma mater and hometown.
He is reportedly in the mix for the UCLA job.