The news comes as a blow to the Knicks, who initially expected Stoudemire to return within two to three weeks after he ruptured a popliteal cyst behind the knee during the Knicks' exhibition game against Toronto on Oct. 19.
But after Stoudemire received a second opinion over the weekend from Dr. Thomas Carter, the Phoenix Suns team doctor, it was determined he would need more time to heal. Carter performed microfracture surgery on Stoudemire's left knee in 2005.
It is not clear whether Stoudemire will use the extra time off to have a procedure or for rest and rehab.
Stoudemire may be out between 6-8 weeks, according to two of the sources.
The Knicks, who open the season Thursday at Brooklyn, are expected to make an official announcement on Tuesday.
Stoudemire's knee problems are no surprise to many league officials. When he was a free agent in 2010, his history of knee injuries scared off most teams and only the Knicks were willing to offer him a five-year, $100 million contract. Because of the condition of his knees, the contract is uninsured.