According to Adrian Wojnarowski of The Vertical, talks are still ongoing but there is "no immediate resolution expected."
The Cavaliers parted ways with general manager David Griffin last Monday after the organization was unwilling to provide him with a contract extension. Wojnarowski immediately reported Billups as a potential replacement thanks to his previous relationship with both owner Dan Gilbert and head coach Tyronn Lue.
Brian Windhorst of ESPN noted Billups was "conflicted" about accepting the position, noting he also had an interview with the Atlanta Hawks.
It would be a major step for the 40-year-old, who has no front-office experience. He spent 17 years in the NBA and played for seven organizations, winning the NBA championship in 2004 with the Detroit Pistons.
He has worked for ESPN since 2014 and signed a new multi-year deal with the company in May.