Jalen Rose does not think the Heat have enough to offer the Timberwolves to land Jimmy Butler. (1:48)

The Minnesota Timberwolves and Miami Heat advanced to the brink of a blockbuster trade for All-Star forward Jimmy Butler over the weekend -- only for the deal to fracture before completion, league sources told ESPN.

Minnesota had shared Butler's medical information with Miami late in the week, sources said, a typical last step before finalizing a trade.

Minnesota owner Glen Taylor and Miami owner Micky Arison had become involved in the talks and there was hope that a trade call with the league office could finalize a deal soon, until Minnesota moved to amend the framework of the trade and talks collapsed Saturday, league sources said.

Minnesota and Miami had been discussing deals that included a third team to take on salary, as well as doing a direct trade between the Timberwolves and Heat, league sources said. Miami had softened on including guard Josh Richardson in versions of a possible deal for Butler, only to recoil once Minnesota pushed late for a sweeter return on the four-time All-Star forward, league sources said.

Talks between the two teams could restart again, but it appears there would need to be a resetting process, league sources said. Minnesota hasn't been engaged in serious talks elsewhere on Butler, with teams' belief that a Miami deal was inevitable and the Timberwolves' steep asking price often remaining nonstarters, league sources said.

Butler is a four-time All-Star who has told Minnesota that he'll leave in free agency in July and wants a trade now.

Taylor is pushing president of basketball operations and coach Tom Thibodeau and general manager Scott Layden to find a deal sooner rather than later for Butler, league sources said.

Minnesota had pushed Miami to include the 25-year-old Richardson -- widely considered a strong two-way player -- in any proposed deal. Richardson, who averaged 12.9 points in 81 starts last season, is in the first season of a four-year, $42 million contract.

Miami's believed willingness to pay Butler something in the neighborhood of a five-year, $190 million maximum contract next summer has played a part in Butler's enthusiasm in pursuing a deal there, league sources said. Miami would acquire Butler's Bird Rights in a trade and could exceed the salary cap to re-sign him.

Miami had been searching for a third team to reroute a contract, which included conversations on Miami guard Dion Waiters, sources said. Incentivizing a third team with draft picks became one of the road blocks in Minnesota completing the trade, league sources said.

In any Butler deal, Minnesota had hoped to unload center Gorgui Dieng and the $48 million left on his contract.

Butler has also expressed interest in several teams with max salary-cap space, including the LA Clippers, Brooklyn Nets and New York Knicks. The Clippers and Nets never found traction in conversations with Minnesota, and the Knicks never called, sources said.

Houston has also been aggressive in trading 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.

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 out West last week, Butler has been working out at the team's facility and has been in regular contact with teammates.