Stoudemire, speaking at his basketball camp Tuesday, said he deserves a maximum contract and would like it to be with Phoenix, where he has played since he was drafted out of high school in 2002. The All-Star power forward said there was "no chance" he would exercise the final year of his contract with the Suns, which would pay him about $17 million.
Phoenix could give him more than any other team -- a six-year deal worth about $127 million.
"We've got the fans excited about basketball again," Stoudemire said. "So what I don't want is for me to have to leave and the fans are now not quite as excited about the game here. I want to keep the hype, want to keep the fans involved, want to keep everybody ecstatic about the Phoenix Suns."
Stoudemire, who helped the Suns reach the Western Conference finals, can become a free agent on July 1 but indicated he would like to have things settled with the Suns before then.
Asked if he would be a Sun if he was offered a maximum deal, Stoudemire said, "There's a very great chance of that."
Stoudemire said his agent, Happy Walters, would meet soon with Suns owner Robert Sarver and general manager Steve Kerr.
"My agent is doing a good job of keeping the line of communication open with Steve Kerr and Robert," Stoudemire said. "Those guys became great friends, so I'll just sit back and let them handle it. Once it comes down to a bottom line, that's when I step in."
Sarver has said he doesn't mind spending the cash as long as he gets his money's worth. Whether that means a full deal for Stoudemire, perhaps a shorter-term contract or nothing at all remains to be seen.
"That meeting's going to tell a lot," Stoudemire said.
Kerr did not return a message on his cell phone.
Stoudemire averaged 23.1 points and 8.9 rebounds last season and was especially effective after the Suns decided against trading him at the All-Star break. He averaged 21.2 points in the playoffs but only 6.6 rebounds.
There is concern by some that Stoudemire eventually will need another operation on his left knee, after he missed virtually all the 2005-06 season following microfracture surgery. He also was sidelined the final months of the 2008-09 season after surgery for a detached retina.
Stoudemire, with career averages of 21.4 points and 8.9 rebounds, cited the success the team has had in his eight seasons in Phoenix.
"The most important factor of playing for an organization is to be able to be totally comfortable and give them 100 percent," he said. "That's what I've done my whole career, so it's only right to look for a maximum contract. From the time that I was here we've done great. We've done great in the community, three Western Conference finals, we've been in the playoffs and won 60 games or so in several years."
Stoudemire was confident there would be plenty of interest should be become a free agent. He mentioned the near-trade as evidence.
"Now there's a chance to get me without giving up players," he said. "I'm pretty sure there's going to be a recruiting frenzy, but again it could not get to that point. You never know."