Shams Charania of Stadium and The Athletic reported the update Friday, noting the sides are expected to "meet in near future."
Billups, who earned the nickname "Mr. Big Shot" during his 17-year NBA playing career, is best known for his eight seasons with the Detroit Pistons. He also made stops with the Wolves, Boston Celtics, Toronto Raptors, Denver Nuggets, New York Knicks and Los Angeles Clippers.
The 42-year-old University of Colorado product retired from the NBA in 2014 after building a resume highlighted by winning the 2004 NBA Finals MVP for the Pistons' triumph over the Los Angeles Lakers.
Billups spent two years as a member of the Killer 3's in the BIG3 basketball league before retiring from all on-court competition last month. He's also served as an ESPN NBA analyst.
Meanwhile, the Timberwolves are looking to fill the key front-office void after firing Tom Thibodeau, who served as both head coach and president of basketball operations, in January.
Minnesota finished the regular season with a 36-46 record, which was 12 games short of a playoff berth in the highly competitive Western Conference.
The Wolves haven't decided the fate of interim head coach Ryan Saunders, but owner Glen Taylor spoke highly of him in a February interview with Sid Hartman of the Star Tribune.
"I think he has a good chance [to get the job full-time]," Taylor said. "It's like everything, we're going to wait until we play out these last 20-some games and I think we'll know and he'll know at that time if it works out. But he is off to a good start."
On Tuesday, Adrian Wojnarowski of ESPN.com reported Los Angeles Clippers general manager Michael Winger was another candidate to become Timberwolves president. Woj noted Brooklyn Nets assistant GM Trajan Langdon is also set to interview for the job.
Minnesota hasn't announced a timetable for a decision.