Rose, 28, will be a free agent for the first time in his career after spending last season with the New York Knicks.
Rose averaged 18 points, 4.4 assists and 3.8 rebounds in 64 games for New York, which finished the season a disappointing 31-51.
Rose is coming off a meniscus tear in his left knee that required season-ending surgery. At the time of surgery, the Knicks offered a timeline for recovery of three to six weeks, so Rose is expected to be fully recovered at this time.
Rose, the 2011 MVP, has a strong relationship with Timberwolves president and head coach Tom Thibodeau; he played for five seasons under Thibodeau with the Chicago Bulls.
The Timberwolves and Knicks discussed a potential trade before the deadline for a package headlined by Rose and Minnesota point guard Ricky Rubio, but no agreement was reached.
Rose and his agent, B.J. Armstrong, have both said that they'd be open to re-signing with the Knicks. In his season-ending news conference, team president Phil Jackson said he was impressed by Rose expressing a desire to return despite the difficult season.
"He enjoyed playing here even with the losses, which of course surprises us because he's been on some very successful teams," Jackson said. "But he wants to redeem himself as a player. Which I like that attitude. I like who Derrick represents as himself. He's very direct about taking on a big challenge."
Toward the end of the regular season, sources told ESPN that the Knicks hadn't ruled out the possibility of re-signing Rose this summer.
It is unclear at this point which other teams besides the Timberwolves view Rose as a potential free-agent target. Some rival executives believe that the San Antonio Spurs may have interest in Rose, depending on how the free-agent market for point guards develops.
Rose, who has a history of serious knee injuries, said in late March that he'd prioritize winning over money as a free agent.
"Not even thinking money. I've got more than enough money saved. If I stopped playing basketball now, I'll be all right," Rose told reporters in Utah on Wednesday night. "I want to win. I want to be happy and feel at peace with myself wherever I'm at. But being at the negotiating table, you never know. I'm not going to negotiate with people where money is the No. 1 thing I'm asking for. I want to win."