Stoudemire, who was in the final season of a five-year, $99.7 million contract, intends to sign with a team in playoff contention after clearing waivers.
Sources with knowledge of his thinking told ESPN.com that Stoudemire is leaning toward signing with the Dallas Mavericks at this point. Another source told ESPNDallas.com that the Los Angeles Clippers and Phoenix Suns have also expressed interest.
The New York Daily News earlier reported the news of Stoudemire's buyout agreement.
Stoudemire will be officially waived Monday and would thus clear waivers Wednesday at 5 p.m., freeing him to sign with another team.
Claiming Stoudemire off waivers would require that team to absorb Stoudemire's $23.4 million salary, which essentially rules out that scenario.
Sources told ESPN.com the Golden State Warriors, Memphis Grizzlies, Portland Trail Blazers and Cleveland Cavaliers -- all playoff contenders in the market for extra size -- are not actively pursuing Stoudemire.
Stoudemire, who was in the final season of a five-year, $99.7 million contract with the Knicks, had said he would spend the All-Star break pondering his future, specifically whether to ask the last-place Knicks for a buyout to give him an opportunity to join a team in the playoff hunt.
"It's not an easy decision to make," Stoudemire told Yahoo! Sports. "Over time, we will see how things pan out. You give yourself a break during the All-Star break. You think about it with your family. ... That will give me a good solid week on how to weigh out the rest of the season."
The Mavs can offer Stoudemire only the veteran's minimum, but he likely would have a significant role off the bench as a candidate for minutes at power forward and center behind Dirk Nowitzki and Tyson Chandler.
"He would fit in great because we play a lot of pick-and-roll," Chandler, who played with Stoudemire in New York the past three seasons, said recently. "Coach [Rick Carlisle] does an excellent job understanding scorers and how to get them the ball and putting them in a position to succeed. Not only that, we've got the best training staff in the league. That also helps."
The 6-foot-10 Stoudemire, a six-time All-Star, has averaged 12.0 points and 6.8 rebounds in 36 games for the Knicks this season despite dealing with a variety of injuries. He missed 14 of the previous 18 games -- because of ankle, wrist and knee injuries -- before returning in a Feb. 6 loss to the Brooklyn Nets.
Stoudemire, 32, has said the decision to request a buyout would be difficult because of his loyalty to Knicks owner Jim Dolan. But he likewise acknowledged in the Yahoo! interview that the constant losing has made it hard for him to remain motivated while playing for the Knicks.
"All possibilities at this point are still open," Stoudemire said last week. "The door is still open for that. But at the same time, I am with the Knicks now. I got to stay optimistic about things and what we are doing here. I can't really focus on the future, because it's not here.
"We still have a couple weeks left before it's all said and done. It's a decision I have to make with my family to figure out the best scenario for the near future."
Carmelo Anthony heard about Stoudemire's buyout shortly after Sunday's All-Star Game.
"One of the main reasons I'm a New York Knick today was because of him. To see him leave, to see the situation where it's at today, I know what he wants and you have to respect that as an athlete as a competitor," Anthony said. "... When he came [to New York] he brought back some excitement to the game of basketball here in New York. There was hope when he came back. People started believing in the New York Knicks again. He was the main reason for that belief and for that hope."
Information from ESPNNewYork.com's Ian Begley was used in this report.