It may not be up to him, or even the Jazz entirely.
Kirilenko was mentioned last week in a potential four-team trade centered around Denver Nuggets star Carmelo Anthony, but so far no deal had been done as Kirilenko and his Jazz teammates posed for pictures and spoke to reporters on the eve of training camp.
"I want to be here. That's the bottom line," said Kirilenko, who has been with the Jazz longer than any other player on the roster. "I want to be part of the Jazz. I'm very pleased to be in this city and playing with the Jazz."
Kirilenko is entering his 10th season in Utah and is scheduled to make almost $18 million in the final year of a contract extension he signed in 2004. His salary makes him an obvious trade candidate, but he is also the most versatile player on the team and right now the Jazz seem content to focus on the team's potential with Kirilenko rather than how much money they could save without him.
"There's always part of a financial picture to everything, but I don't think that we went into this season with the idea that we needed to trade Andrei," general manager Kevin O'Connor said.
O'Connor acknowledged there have been inquiries from other teams about Kirilenko, but would not comment on reports of the megadeal that surfaced late last week.
O'Connor said the situation is a lot like the one the Jazz faced a year ago when Carlos Boozer reported for the final year of his contract after a summer of speculation he would be traded. The Jazz were unwilling to give up their leading scorer and rebounder without getting something in return just to avoid a luxury tax hit.
"We've never initiated a trade call this whole summer about AK," O'Connor said.
But the Jazz are willing to listen and if another club makes the right offer, Kirilenko could be playing elsewhere for the first time in his NBA career.
Kirilenko has averaged 12.4 points in his career with the Jazz and his 1,306 blocked shots are the second most in team history.
"I don't think there's anybody on the team that can do the things he does. He brings a different set of intangibles than anybody on this team," said point guard Deron Williams, who quickly grew tired of questions about Kirilenko's future.
"Is AK here? He's here today?," Williams said. "As of right now, he's with us tomorrow, right? When it comes across the ticker that AK has been traded, then come ask me questions. Until then I'm not going to talk about it."
With center Mehmet Okur still recovering from surgery to repair a ruptured Achilles tendon in April and several new additions to the roster, coach Jerry Sloan would like to see Kirilenko stay.
With or without Kirilenko, the Jazz had more turnover this summer than they had in years.
Boozer, Kyle Korver and Wesley Matthews all left as free agents. The Jazz quickly picked up center/forward Al Jefferson and brought back veteran guard Raja Bell, who played two years in Utah. Utah also added veteran point guard Earl Watson on Sunday and will have rookie Gordon Hayward trying to learn the system after leaving Butler early for the NBA draft.
Sloan, entering his 23rd season coaching the Jazz, said that's plenty of change to deal with as the team enters training camp.
"We want Andrei here. He's a huge part of what we've done and we need him," Sloan said.