In an attempt to add Love, a three-time All-Star, the Cavaliers are willing to part with Andrew Wiggins and Anthony Bennett.
One source said the Cavs also are willing to give up a first-round draft pick for next season. Any other players involved in the talks are not known.
At one point, a trade seemed close to happening, but Minnesota wants more than the Cavaliers are currently offering, sources said.
Wiggins and Bennett were held out of the Cavaliers' summer league finale Friday night against the Miami Heat.
The Cavs said both players would warm up and were dressed, but that they had already given the team all it needed to see in four previous games in Las Vegas.
The Timberwolves are also engaged in talks with the Golden State Warriors, who have been pursuing Love for several weeks.
The Warriors have thus far been unwilling to offer Klay Thompson, and are currently dangling David Lee and Harrison Barnes.
While some executives in Golden State are willing to part with Thompson, the club's overall stance has been that he will not be traded.
There is also a feeling around the league that Minnesota is attempting to drive up the price for Love by having the Cavs and Warriors compete for the deal.
Information from The Associated Press was used in this report.
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