"I spoke to the doctor," Kirilenko said, "and maybe it will be Saturday. Not for sure. Nobody knows for sure. . . . But it's getting better every day. It feels very good now. So Saturday, maybe."
Without Kirilenko, the Jazz lost 18 of 21 games before their 97-96 win over San Antonio at the Delta Center.
Utah plays host to Phoenix on Wednesday, travels to Sacramento on Thursday and entertains LeBron James and the Cleveland Cavaliers on Saturday.
That's when Kirilenko hopes to come back from the injury, which he suffered in an early-season 109-76 loss at San Antonio.
Matt Harpring and Raja Bell also missed the win over San Antonio because of injuries.
Harpring was sidelined with a sore knee, which was drained Sunday. He plans on returning against Phoenix, calling his absence against the Spurs "more of a precaution than anything else."
Bell missed his fifth straight game, also with a sore knee. He could also return against the Suns.
Because of the injuries, Jazz coach Jerry Sloan started Keith McLeod, Gordan Giricek, Curtis Borchardt, Carlos Boozer and Kirk Snyder against San Antonio.
Sloan has now used 11 different starting lineups this season.
In all, the Jazz have missed a total of 123 player-games because of injuries, led by Kirilenko (22) and Raul Lopez (18).
For Snyder, his start against the Spurs was the second of his career.
He ended up playing 29 minutes - only one shy of his season high. He had seven points and, because Giricek fouled out, Snyder was on the floor when Mehmet Okur scored his game-winning rebound after a miss by McLeod.
"I just tried to space out," he said. "I tried to make them make a decision: 'Do I go into the lane and help. Or do I stay outside?'
At last, clank
The Jazz had a streak of 31 straight free throws made snapped when Lopez missed one with 3:16 left in the second quarter against the Spurs.
The Jazz had made their final nine free throws in an 84-78 loss at Chicago on Friday. They made 17 straight in their 89-86 loss at Milwaukee on Saturday. They made five straight before Lopez's miss against the Spurs.
Individually, Okur has made 63 of his last 69 free throws, including nine out of 10 against the Spurs.