Rose, a free agent this summer, played for seven seasons under current Timberwolves and ex- Chicago Bulls coach Tom Thibodeau.
It is unclear what Minnesota would offer in a potential trade for Rose. Sources say the Timberwolves are motivated to trade veteran point guard Ricky Rubio, as team president and coach Thibodeau sees rookie Kris Dunn as the point guard of the future for Minnesota.
The Timberwolves, sources say, are among several teams to reach out to the Knicks asking about potential trades for Rose.
The NBA trade deadline is Thursday at 3 p.m. ET.
Rose, in his first season in New York, is averaging 17.7 points per game on 46 percent shooting in 48 games. He has missed time due to back spasms and an ankle injury, but Rose's knees, which caused him to miss major portions of recent seasons, have been healthy.
Knicks president Phil Jackson traded for Rose last summer, the first move made to compile a roster that the organization hoped would compete for a playoff spot.
The Knicks (23-34) have struggled thus far. They are four games out of eighth place in the Eastern Conference and have lost seven of their past 10 games.
ESPN's Brian Windhorst contributed to this report.