Adrian Wojnarowski talks about Jimmy Butler's desire to play for the LA Clippers and the likelihood the deal gets done before training camp. (1:30)

Rival executives lobbing calls to Minnesota's front office on the possibility of trading for four-time All-Star forward Jimmy Butler are getting their inquiries rebuffed, league sources told ESPN.

In the aftermath of Butler's trade request this week, Minnesota executives are telling teams that Butler's an elite player and that the franchise intends to keep him, league sources said.

Often that's an opening message that's followed with a query on what a prospective trade partner might offer in a hypothetical deal, but that hasn't been the case in the Timberwolves' dialogues with teams late this week, sources said.

Nevertheless, Timberwolves owner Glen Taylor has become fully engaged in the decision-making process on a potential Butler trade and is far more open to the idea of orchestrating a deal than president of basketball operations Tom Thibodeau and GM Scott Layden, league sources said.

Opposing teams believe the fastest avenue to a Butler deal is engaging Taylor, league sources said. Taylor is attending the NBA's Board of Governors meetings today in New York, which include owners and top basketball executives.

Taylor has overseen high-profile Minnesota stars getting traded in the past, including Kevin Garnett and Kevin Love.

Thibodeau is less inclined to trade Butler, especially in a scenario that would imperil the franchise's ability to reach the playoffs for a second straight year after missing the postseason the previous 13 seasons, league sources said. Thibodeau's initial reaction to the trade request was that he wanted to win now, and trading Butler would almost assuredly bring back a package that would diminish the Timberwolves' chances in the short term, league sources said.

Butler, 29, prefers a trade to the LA Clippers, and has a strong interest with the New York Knicks as well as an interest with the Brooklyn Nets, league sources said. Those three teams have the salary-cap space to sign Butler outright this summer to a maximum contract extension.

Butler told Thibodeau that he would like to be traded before reporting for Timberwolves media day on Monday and that he plans to leave the franchise in free agency next summer, league sources said.

The Clippers have two max contract slots available in July. They are emerging as a front-runner for Kawhi Leonard when Toronto's All-NBA forward becomes a free agent in July, league sources said.

The Nets' ability to sign two max free agents in the summer will keep them in consideration for Butler, but he has prioritized the Clippers and Knicks over them, league sources said.

The Clippers have a roster that includes a blend of good, hard-playing veterans (Tobias Harris, Patrick Beverley and Lou Williams) and talented young guards who could appeal to Thibodeau's desire to surround All-Star center Karl-Anthony Towns and forward Andrew Wiggins with playoff-competent talent.

Nevertheless, it remains uncertain how much -- if anything -- the Clippers would trade for a player whom the team could sign this summer without surrendering any assets.

In any circumstance, Butler wants a trade to a team that plans to sign him to a five-year, maximum contract that could be worth $190 million in the summer, and his list could expand based upon the Timberwolves' and rival teams' willingness to negotiate a trade for him, league sources said.

The Miami Heat have been interested in Butler too, league sources said, although the Heat don't have the salary-cap space in July to pursue him.

Butler will join a free-agent class that could include Leonard, Kevin Durant, Kyrie Irving, Klay Thompson, DeMarcus Cousins, DeAndre Jordan and Kemba Walker. The market for Butler will likely be the five-year, $190 million maximum extension that could come with a trade to a new team, which means a team would be committing $40 million-plus annually to Butler as he reaches his mid-30s.

Butler is downplaying his fractured relationship with Towns as a reason for wanting a trade, league sources said.

Thibodeau traded recent first-round picks -- including Kris Dunn, Zach LaVine and the No. 7 pick that became Lauri Markkanen -- in a 2017 deal with the Chicago Bulls to acquire Butler.

Butler, a four-time All-Star, is one of the league's elite two-way players. He averaged 22.2 points, 5.3 rebounds and 4.9 assists for the Timberwolves last season.