Stoudemire, who has a ruptured cyst in the knee, originally was scheduled to return in 10 to 17 days.
"He could still be back in two weeks, but they don't know," the league source said.
The New York Daily News earlier reported that Stoudemire would be going for a second opinion on the knee. The paper reported that Stoudemire could miss the first month of the season.
The Knicks' original timetable stated that Stoudemire would miss anywhere from the first four to 11 days of the season.
Tweeted Stoudemire's agent, Happy Walters, on Saturday: "To all of the Knicks fans sending me messages... Stat will be fine. He's working w/ team trainers - will b back ASAP.
"No 1 wants to b out there after working all summer on his game more than Stat, himself."
The Knicks open the regular season on the road Thursday against the Brooklyn Nets.
Stoudemire first injured his knee in a practice collision with teammate Chris Copeland. The Knicks originally called it a bone bruise but following an MRI, it was later determined that Stoudemire had ruptured a popliteal cyst behind his left knee.
Stoudemire's left knee has been an issue in the past. He underwent microfracture surgery in October 2005, but bounced back well from the procedure.
One NBA team doctor told ESPNNewYork.com that Stoudemire was the best example of a player regaining his form after microfracture surgery.
Still, the procedure can be a red flag for teams. Stoudemire's contract with the Knicks -- a five-year, $100 million pact -- is uninsured because of his history of knee issues.
Stoudemire seemed to be in great shape going into training camp, ready to bounce back from a trying 2011-12 campaign.