Garnett, drafted fifth overall by the Wolves in 1995, is in his second season with the Brooklyn Nets – his 19th season in the NBA.
Stein reports the Wolves are looking to trade forward Thaddeus Young for Garnett. Young has a player option next season for about $10 million, according to Rotoworld.
The NBA trade deadline strikes at 2 p.m. CT Thursday.
More from Stein:
"Sources told ESPN.com that the sides have engaged in serious discussions on the deal, which would ultimately require Garnett's approval even if the teams ultimately agree before Thursday's 3 p.m. deadline, since Garnett possesses one of the NBA's six active no-trade clauses in the league.
"Garnett has insisted in recent weeks that he is not in the market for an in-season exit from Brooklyn, largely because he does not wish to displace his family in the middle of the season."
But the Wolves hope Garnett's affinity for Minnesota will be enough to encourage the 15-time All-Star to waive his no-trade clause. Stein says Garnett is still very close to Timberwolves head coach Flip Saunders, who coached Garnett from 1995-2005.
Garnett spent 12 seasons with the Wolves before being traded to the Boston Celtics in 2007. KG won a title with the Celtics in 2007-08.
The 6-foot-11 forward from Farragut Academy in Chicago is averaging 6.8 points and 6.8 rebounds per game this season.
Garnett has made more than $300 million in salary during his career and according to Yahoo Sports, he is interested in someday becoming part-owner of the Timberwolves.
"I want to buy the Timberwolves. Put a group together and perhaps some day try to buy the team. That's what I want," Garnett told Yahoo in November.