The deadline indeed passed at 3 p.m. Thursday afternoon with Stoudemire still in Phoenix, but only after the Suns and Houston Rockets engaged in 11th-hour discussions, according to sources close to the situation.
One source told ESPN.com's J.A. Adande that the Rockets -- fresh off constructing a three-team blockbuster that sent Tracy McGrady to New York and landed Kevin Martin in Houston -- offered veterans Shane Battier and Luis Scola, multiple draft picks and the expiring contract of Brian Cook for Stoudemire. But the source said Phoenix wanted to waive the requisite physical examinations for the players involved to make sure the trade went through in time, only for Houston to refuse because of Stoudemire's injury history.
Yet another source with knowledge of the talks disputed that account, telling ESPN.com that the Suns initiated the conversation by asking for Battier, Scola and draft considerations, which Houston refused.
It was just the latest episode in the Suns' on-again, off-again shopping of Stoudemire, who has been aggressively made available and then not traded in two successive Februarys.
"I am still a member of the Suns," Stoudemire said on his Web site. "I am with a great team and coaches.
"It was nice to have other teams and players want me to join their teams, but I am happy to stay in Phoenix. I appreciated all the Suns' fans across the country who reached out to me and showed the love and support. Everything happens for a reason."
ESPN.com's Chad Ford -- who reported earlier Thursday that an unspecified new suitor was making a late bid for Stoudemire -- reported after the deadline that Sarver and Suns president Steve Kerr were scheduled to go to dinner Thursday night with Stoudemire and agent Happy Walters. The meal was planned as an attempt to start mending fences after Stoudemire was so openly shopped in potential deals with Cleveland, Miami and Philadelphia before the Houston scenario.
It was not immediately known if the sides intend to resume talks on a contract extension before Stoudemire has the chance in June to opt out of the final year of his contract or if Stoudemire is determined to leave at season's end no matter what. The camps recently exchanged proposals on an extension during All-Star Weekend in Dallas but did not get close to an agreement.
In an e-mail to ESPN.com earlier Thursday, Sarver confirmed reports in The Arizona Republic and on FanHouse.com that he met privately with Stoudemire after Wednesday's loss in Dallas to let him know that the Suns were no longer looking to move him.
"I think I'm pretty much safe," Stoudemire told FanHouse on Wednesday night after his brief chat with Sarver. "I feel good about it. But I would have felt good either way."
Walters, echoed that view in an interview Thursday morning with ESPN.com's Ford, saying: "The better [Stoudemire] played over the last couple of weeks, the more emboldened the team got with trades. Anything can happen, but it seems unlikely."
Stoudemire has averaged 26.6 points and 11.7 rebounds the past seven games and started for the West in Sunday's All-Star Game.
The Cleveland Cavaliers pursued Stoudemire hard in recent days at the behest of LeBron James, but pulled out of talks with the Suns Wednesday afternoon and swung a three-team deal instead for Washington's Antawn Jamison when Phoenix told the Cavs it wasn't ready to commit to a Stoudemire trade.
The Miami Heat were the last known suitor left for Stoudemire, but sources say Miami was not willing to add Michael Beasley to a trade package. Although the Suns, according to sources, saw Beasley more as an asset for down-the-road moves than as a potential piece of their long-term future, they wanted Beasley and at least one future first-round pick before they surrender Stoudemire.
Ford reported that the Heat were willing to offer one of their two first-round picks this June, but Miami built the rest of its Stoudemire offer around the expiring contracts of Udonis Haslem and ex-Suns swingman Quentin Richardson, keeping Beasley out of the deal.
Sources say the Heat ultimately decided that it's better to wait until the offseason to try to sign Stoudemire outright as opposed to surrendering an asset like Beasley to get him now. Miami will have the requisite salary-cap space this summer to try to sign Stoudemire and pair him with star guard Dwyane Wade, as long as Stoudemire opts out of the $17.7 million he's owed next season to become an unrestricted free agent.
The Suns had been hoping for weeks to land Philadelphia's Andre Iguodala in a Stoudemire deal, but NBA front-office sources maintain that the 76ers never relented on their unwillingness to let go of Iguodala for Stoudemire, even if Phoenix also takes back the contract of Samuel Dalembert.
Stoudemire told The Arizona Republic that he's finally getting his rhythm back after being restricted to limited activity in the offseason after having eye surgery last February.
"It was tough because I didn't understand the reason behind the trades," Stoudemire told the newspaper after meeting with Sarver. "I didn't know what I was doing wrong. I didn't know what they thought about my game or such. It bothered me there for a bit but I happened to turn on the switch and get back to the ultimate goal, and that's to win ballgames. That allowed me to get back to a high level."
Stoudemire had said before Wednesday's game in Dallas that it "could be my last in a Suns uniform" and has left open the possibility that he will not opt out of the final year of his contract.
Asked by the Republic about his $17.7 million player option if he remains a Sun, Stoudemire said: "If I'm still a Sun after [the deadline], I'm not sure what the future holds. We just have got to patiently wait, I guess."
Still, general manager Steve Kerr said he considered standing pat at Thursday's NBA trade deadline was the best option for the Suns.
"I've maintained that unless there was something out there that improved our team and put us in a lot better position moving forward, then we weren't going to do anything. And that was the case," Kerr said.
"We contemplated a lot of things today. Nothing jumped out, and we move on. Frankly, all of us are kind of relieved, because we are excited about this team. We listened to a lot of people. Multiple teams called us. We called a couple of teams just to inquire about certain things. In the end, nothing really struck our fancy."
At the All-Star festivities, Stoudemire said he wondered why he has been mentioned in trade talks in each of the last two seasons, but Kerr said he did not expect any ill will moving forward.
"It's not easy to have your name mentioned," Kerr said. "It's harder when you are a first-team All-Star, because those guys are not used to having their names thrown around. I don't foresee any problems relationship-wise, but I'm going to talk to him. I expect him to keep playing his heart out."
Kerr and Stoudemire's camp, which includes agent Walters, exchanged ideas on a new contract for Stoudemire earlier this season, and Kerr said he hoped to continue that process.
Walters said he is always open to listening.
"I don't know that we're going to reach an agreement. I've been quoted as saying we're close, but I never said that," Walters said. "Amare is an important part of their future -- it is up to the Suns to say how much.
"We've exchanged ideas. The ball is in their court. It's going to be what he feels the team is going to do in the future. Are they going to build the team, or stay where they are?"
Information from the Associated Press was used in this report