Stoudemire rated his chances of being traded before Thursday's deadline as 50-50.
Speaking before the Phoenix game at Dallas on Wednesday night, Stoudemire said he had not heard anything from the Suns and was just waiting for the deadline to pass at 3 p.m. ET on Thursday.
The All-Star forward said he doesn't necessarily agree with his agent's comments that a trade was imminent.
"It's still 50-50 -- not sure what's going to happen," Stoudemire said. "We have another day or so for it to break down. Like I said, whatever happens I'm going to remain professional, play my heart out on the basketball court."
Cleveland was considered the most likely destination if Stoudemire was dealt. But the Cavaliers moved on to their next choice, according to several reports, acquiring Antawn Jamison from Washington in a three-team trade on Wednesday.
"Cleveland made a decision that I'm sure they felt they needed to make," Stoudemire said, "that they had a better chance of making."
Stoudemire said he would have no hard feelings toward the Suns if he wound up staying.
"It's all about being professional," he said. "My character -- hopefully you guys have been seeing my character over the past 7½ years -- but more so over the last two years with all the trade talks. I'm still going to remain a competitive force on the basketball court if the trade doesn't happen."
Earlier, Stoudemire's agent Happy Walters told The Associated Press that it would make no sense for the Phoenix Suns not to trade Stoudemire only to see him walk away as a free agent at the end of the season.
Walters said Stoudemire believed Phoenix's game Wednesday night at Dallas would be his last for the Suns.
Stoudemire said he had no problem with that comment.
"This could be my last game in a Suns uniform," Stoudemire said, "and it could be many more. You never know."
Stoudemire also said "the door is open" for talks on a long-term contract with Phoenix.
"I can remain with this team another five years or I can be elsewhere another five years," he said. "We're not sure what's going to happen, but my ultimate goal is to eventually contend for a championship and get the best out of our team."
The Suns are not likely to want a contract that extends five years.
Walters said there had been no contract talks with Phoenix since last weekend.
"We're not that far apart," he said, "but I think they've decided to go in another direction."
Miami also has been mentioned as a candidate for a Stoudemire trade, as has Philadelphia, although Walters said that he hasn't heard anything about the 76ers in some time.
Suns general manager Steve Kerr declined to comment. Kerr never has said the team definitely would trade Stoudemire, only that he is listening to offers.
Stoudemire, who has played all eight of his NBA seasons with the Suns, has one year left on his contract but can opt out after this season. If he decides not to opt out, he would earn $17.7 million next season.
The Suns still have several options if they decide not to make a deal now and Kerr has said in the past that no deal would be made unless it made sense for Phoenix.
Stoudemire also could decide not to opt out of the contract and take the $17.7 million, becoming a free agent after one more season with Phoenix. No team probably would match that figure in any long-term deal.
Finally, the Suns could decide to keep the team together for this season regardless of what Stoudemire decides to do.
Entering Wednesday night's play, Phoenix (32-22) was tied with Oklahoma City for fifth in the Western Conference but was only 3½ games from falling out of the playoffs in the tight race. The Suns had won six of seven overall and five in a row on the road.
"I think we're exceeding expectations from the start of the season," Stoudemire said, "so if we continue to improve the way we are then we're going to be OK. There could be possible moves to allow us to contend for a championship sooner than later."
Coach Alvin Gentry said the front office and owner Robert Sarver were not going to make any deal unless it was "for the betterment of our team."
"If we don't trade him, that's because they think we'll be better than the calls that we got," Gentry said. "And if we do trade him, then they think we'll be better. I think it's a real simple thing."
He said the Suns never were saying "'We're going to trade Amare, We're going to trade Amare.' But you have to listen."