He transferred to the University of Cincinnati after his sophomore season, where he played for the basketball team under coach Bob Huggins, along with future NBA players Danny Fortson and Ruben Patterson.
[4] Monroe averaged 3.2 points and 2.9 rebounds per game in the 1995-96 season, backing up Fortson at small forward and helping the team win the Conference USA title and reach the NCAA Elite Eight.
He averaged 4.6 points and 2.5 rebounds in the 1996-97 season, contributing to the team winning the Conference USA title and qualifying for the NCAA Tournament second round.
He became a regular starter at tight end when Josh Anderson suffered a torn ACL against the University of Houston on October 18.
Monroe was selected by the Dallas Cowboys in the seventh round (237th overall) of the 1998 NFL draft.
[14] In the 2001 offseason Monroe was allocated to the Frankfurt Galaxy of NFL Europe, where he caught 23 passes for 362 yards and 2 touchdowns.