Discussions have been ongoing for two weeks, but no trade was close or imminent late Wednesday night, league sources said.
Minnesota's preferences in a Miami deal have included center Bam Adebayo, guard Josh Richardson and a protected 2019 first-round pick, league sources said. A trade could take on a larger construction to include more players, league sources said.
In any Butler deal, Minnesota has wanted to unload center Gorgui Dieng and the $48 million left on his contract.
Timberwolves executives told other interested teams in the past 24 hours that they didn't have any offers that met the franchise's criteria to honor Butler's trade request and planned to hold on to him until a deal met their requirements, league sources said. Miami is one of the preferred destinations of Butler's, league sources said. He has told the Wolves that he'll leave the team in July free agency, and has expressed interest in several teams with max salary space, including the LA Clippers, Brooklyn Nets and New York Knicks.
Houston has also been aggressive in attempting to trade for Butler, sources said. Like Miami, Houston doesn't have the salary-cap space to sign Butler in the summer and needs to acquire him now to obtain his Bird rights to retain him on a new deal in July.
When the Timberwolves return from a West Coast preseason road trip early Thursday morning, president of basketball operations and coach Tom Thibodeau is expected to push for Butler to return to practice and start preparations for the regular season, league sources said.
Butler could return as soon as next week, but hasn't made a decision and is still rehabbing his surgically repaired right wrist, league sources said.
Butler, 29, has expressed no intentions of missing regular-season games if he's healthy to play, league sources said.
So far, Minnesota has allowed Butler to stay away in the preseason; presumably as the team works to find a trade for him. As the Wolves traveled, Butler has been working out at the team's facility and has been in regular contact with teammates.