The framework of the proposed deal is Love and shooting guard Kevin Martin to Golden State for Thompson and power forward David Lee, the source said.
"No deal is close," a league source involved in the trade talks told Yahoo Sports’ Adrian Wojnarowski. “[Pieces] change all the time."
Thompson, who is slated to become a restricted free agent in 2015, would be open to going to Minnesota because he believes it would increase his chances of getting a maximum contract, the source said.
Andrew Bogut, Andre Iguodala and Stephen Curry will each make $10.6 million or more next season, meaning that big money for Thompson, 24, could be hard to come by in Golden State. The contracts of that group aren't set to expire until after the 2016-17 season.
Mychal Thompson, Klay's father who played college basketball at Minnesota before a lengthy NBA career, originally reported that his son had been included in the trade talks.