Sources told ESPN that the agreement would be a combination of a head-coaching extension and a role as an ambassador after his retirement. Details of the contract weren't disclosed.
The extension comes after sources told The Athletic that UCLA had interest in Calipari, offering him a six-year, $48 million deal. Kentucky's lifetime contract offer came in response to UCLA's lucrative proposal.
"Where else would I want to coach?" Calipari said. "It has nothing to do with the other stuff. ... People call every year. They presented it to me and I appreciate it."
Calipari's current contract at Kentucky runs through the 2024 season. He is the highest-paid basketball coach in the country, earning about $9.2 million in total compensation this year, according to USA Today's database of coaching salaries.
The Wildcats posted a 30-7 record this season and earned a No. 2 seed in the NCAA tournament. Kentucky advanced to the Elite Eight before losing to Bruce Pearl and the fifth-seeded Auburn Tigers 77-71 on Sunday.
Calipari has reached the Final Four with Kentucky four times (2011, 2012, 2014-15) and won a national championship in 2012. The Wildcats' loss to Auburn marked the third consecutive season that Kentucky reached the second weekend of the tournament but had fallen short of the Final Four.
The 60-year-old Calipari has posted a 305-71 record at Kentucky. He has a career record of 708-209, leading his teams to the NCAA tournament 20 times in 27 seasons.