Butler joined the Philadelphia 76ers in November after he requested a trade from the Minnesota Timberwolves.
The star had been involved in some controversy with the Wolves, and was involved in an off-court spat with franchise management.
In the summer, he will become an unrestricted free agent, and will be open to listening to offers.
Leonard will also be a free agent this summer, after he was traded from the San Antonio Spurs to the Toronto Raptors last summer.
The futures of the pair are among the most talked-about stories in the NBA, as fans wait to see where the two All-Stars will end up.
Leonard has been linked with a move to either the Los Angeles Lakers or the LA Clippers, but is seemingly happy in Toronto.
He has stayed quiet on his future, and has not publicly declared where he wants to play next year.
However, he is from Los Angeles, and a move to the Clippers could be the most appealing to him as it would give him the chance to lead his own franchise.
And he could be joined there by Butler.
According to Brandon Robinson host of the Scoop B Radio podcast, Butler wants to play alongside Leonard.
“Philadelphia 76ers’ Jimmy Butler “still has a desire to sign with the Los Angeles Clippers this offseason,” I’m hearing this afternoon,” he tweeted.
“Butler is “intrigued by possibly teaming up with Kawhi Leonard.”
Robinson quoted his source as saying “Jimmy would love to play alongside Kawhi in LA with the Clippers.
“Jimmy Loves LA, and as of now, still has his eyes on the Clippers in free agency.”
Both men are able to be traded by their franchises before February 7.
However, it is unlikely that either will leave outside of free agency.