(Jesse Johnson/USA Today Sports)

The Minnesota Timberwolves are starting to realize that their hopes of signing Kevin Love to a contract extension are slim and may be looking to trade him, the Associated Press reports.

Love can opt out of his contract and become an unrestricted free agent after next season. And, after making three all-star teams but missing the playoffs in all six years of his NBA career, he seems poised to do exactly that.

The Timberwolves went 40-42 this season, their most wins since 2004-05 but still not enough to make the playoffs for the first time since 2003-04. They have the second-worst odds in Tuesday night’s draft lottery, with only a 0.6 percent chance of landing the No. 1 pick. Defying the odds and securing a high draft pick —  Minnesota has had dismal luck in the lottery, never moving up once — might be the only way for the Timberwolves to persuade Love to stay.

But Minnesota may be better off getting something in return for Love. “A likely asking price would include a high first-round pick in this year’s draft and a solid veteran or two who would come in and contribute right away to a team that is lacking in veteran leadership,” the AP reports. And any team that trades for Love would probably only do so after getting some sort of indication from Love that he would be willing to sign a max deal after the trade.

That probably narrows down the list of possible destinations for Love.

According to ESPN’s Marc Stein and Ramona Shelburne, Chicago and Golden State “are among the potential trade destinations that intrigue Love,” while the Lakers and Knicks “been mentioned all season as big-market landing spots that would tempt Love, but going to the best situation for immediate contention is said to be the power forward’s priority.” (For the Knicks, there’s also the minor sticking point that — despite “plotting” to get Love to MSG — they don’t have much to offer the Timberwolves.)

Yahoo Sports’ Adrian Wojnarowski also posits that the Celtics are “an increasingly intriguing destination” for Love, depending on where Boston lands in the lottery (the Celtics have the fifth-best chance of getting the No. 1 pick).

Wojnarowski also has Houston as a possible destination, because of Love’s familiarity with Rockets Coach Kevin McHale.