The Timberwolves will receive 2014 number one draft pick Andrew Wiggins in the proposed deal, which is said to also involve the Philadelphia 76ers.
The Sixers will send Thaddeus Young to Minnesota, and receive the top pick from the 2013 draft, Anthony Bennett, from Cleveland.
The sticking point is that Wiggins cannot be traded until August 23rd, as NBA rules prevent a rookie being traded within 30 days of signing a contract.
The supposed agreement was reported by Brian Windhorst in an interview with ESPN radio.
"The deal is done but not done," Windhorst said. "The teams have agreed, but they can’t say they have agreed and they can’t agree, because we’re in this weird moratorium period because you can’t trade Andrew Wiggins until the 23rd of this month.
"So, between now and then – which is, what, 19 days – could some of that happen? Could a team come in with a trade that maybe Minnesota doesn’t see? Yes, it could happen. So therefore it is not done."
Windhorst that adamant that although there are many moving parts in this trade and a late swerve could still occur, it is almost guaranteed that Wiggins and Love switch teams.
He said: "Essentially what you need to know if you’re an NBA fan, Kevin Love is going to be on the Cavs barring anything unforeseen, and and Andrew Wiggins, No. 1 overall pick, is going to be on Minnesota."
Last week Timberwolves owner Glen Taylor said that a Love trade would be completed by the end of August. Windhorst's report seems to confirm that it will be the Cavaliers, as expected, who capture the all-star big man.