Mack, 44, has led the Musketeers to the NCAA tournament in four of his five seasons since taking over for Sean Miller in 2009. Xavier reached the Sweet 16 in 2010 and 2012.
Coach Mike Montgomery retired earlier this month after six seasons in Berkeley. The 67-year-old had previously been coach at Montana, Stanford and with the Golden State Warriors. He has publicly pushed for assistant Travis DeCuire to get the job.