The Heat emerged from the All-Star break even more determined than they were before to find a third team to help them broker an Amare deal before Thursday's 3 p.m. deadline.
Miami is "coming hard" after Stoudemire, one source said.
Although the Heat have first-round picks available to sweeten any Stoudemire deal -- with the Suns hoping to come away with at least one first-rounder if they decide to trade Stoudemire this week -- sources say Phoenix has no interest in taking back Jermaine O'Neal's hefty expiring contract because, at $23 million, it requires more players to be worked into the deal than the Suns are comfortable with.
Yet one source insisted Monday night that the Suns have not ruled out taking back forward Michael Beasley as part of a Stoudemire deal. The Heat -- after carefully preserving their salary-cap space for months -- are suddenly pushing hard to make a big trade splash now if possible instead of waiting for free agency in July and gambling on the idea that they can lure a marquee name such as LeBron James or Chris Bosh to South Beach to flank Dwyane Wade.
The Cavaliers are prepared to send Zydrunas Ilgauskas' expiring contract, young power forward J.J. Hickson and perhaps draft considerations to the Suns for Stoudemire, who appeared to give Cleveland further motivation to make that bold move when he used his Twitter feed Monday night to scoff at speculation that he and Cavs center Shaquille O'Neal can't coexist.
"You guys can stop saying we don't play well together," Stoudemire tweeted.
A pick from the perennially contending Cavs obviously wouldn't be as enticing as a Miami draft pick, but sources say that Cleveland also continues to chase longtime target Antawn Jamison in case Miami assembles a better deal for Stoudemire. It likewise remains to be seen whether Philadelphia decides to make Andre Iguodala available after making it clear before the All-Star break that it is not prepared to surrender Iguodala in a Stoudemire deal.
"They're the wild card," one source said of the Sixers.
The Cavs resume play Thursday at home against Denver riding a 13-game win streak, but they still hope to come away with a big player by week's end. While Stoudemire leads their list, the Cavs have also been mentioned in relation to Washington's Jamison and Indiana's Troy Murphy. Sources told ESPN The Magazine's Chris Broussard on Monday that the Cavs are also in talks with the Warriors about Corey Maggette.
The Suns, meanwhile, appear intent on finally finding a workable trade for Stoudemire before the deadline -- even though the sides did briefly discuss a contract extension during All-Star Weekend in Dallas -- after shopping him heavily at last season's trading deadline as well. Stoudemire is averaging 21.2 points and 8.6 rebounds this season and started at center for the West in Sunday's All-Star Game.
Senior writer Marc Stein covers the NBA for ESPN.com.