Crawford, one of the league's elite reserves, will be opting out of a guaranteed salary of $4.5 million to test free agency.
He agreed to a two-year, $9 million pact with the Timberwolves last offseason after reaching a buyout from the Atlanta Hawks.
Crawford was a vital force down the stretch of the regular season in helping Minnesota claim its first playoff berth since 2004.
The 38-year-old guard is the only player in NBA history to have won the Sixth Man of the Year award three times.
Guard Jimmy Butler has stressed to management that he wants Crawford to remain in Minnesota by any means necessary, sources said.
Over his 18-year career, Crawford also has played for Chicago, New York, Golden State, Atlanta, Portland and the LA Clippers. He was the eighth overall pick for Cleveland in the 2000 NBA draft out of Michigan.
During the 2017-18 campaign, the 6-foot-5 guard averaged 10.3 points and shot 47 percent from the field in 80 contests -- and all were off the bench.