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.
The Timberwolves are also engaged in talks with the Golden State Warriors, who have been pursuing Love for several weeks.
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.