A statement released by University of Minnesota Athletics Director Norwood Teague indicated the school and Pitino have an understanding "on the key terms of an agreement," which he said would be finalized this week.
If the deal is completed, Pitino, 30, would take over from the fired Tubby Smith.
Pitino would come to Golden Gophers after completing one season as head coach of the Florida International University Panthers, whom he guided to an 18-14 record -- FIU's first winning season in 13 years.
Before that he served as his father's associate head coach at Louisville, his second stint with the Cardinals. He also served as an assistant coach for Louisville from 2007-09.
In between, Pitino was an assistant coach for the Florida Gators.
Smith was fired after Minnesota went 21-13 this past season, ending with a loss to Florida in their second game of the NCAA Tournament.
Smith was subsequently hired to lead Texas Tech.