Stoudemire will not play on Tuesday against Boston and is unlikely to play on Wednesday in New Jersey. But there is a possibility that he returns to the team later this weekend, either Friday night against Cleveland or Sunday against Atlanta, according to the source.
"It's a possibility," the source said.
The team would like to see Stoudemire improve his conditioning and test his injury in a game setting before he suits up. Stoudemire was able to do that in practice on Saturday, scrimmaging 4-on-4 with his teammates.
He may have another opportunity to scrimmage on Thursday before the Knicks travel to Cleveland.
Stoudemire had previously been working out and shooting before games with assistant coach Kenny Atkinson. Thursday's workout was his first with teammates since he last played on March 24. He left that night's game against Detroit with back pain, which was later diagnosed as a bulging disk in his lower back.
Stoudemire had an epidural shot to relieve the pain on March 29. The team originally said he'd be out two to four weeks. Thursday was two weeks from the day of the shot.
The Knicks have gone 7-4 in Stoudemire's absence. Jeremy Lin has been out over the same stretch of games due to a meniscus tear in his knee. In their absence, the Knicks have relied heavily on Carmelo Anthony.
And Anthony has responded, scoring 33 points on 52 percent shooting in the past 11 games -- a significant increase from his season averages of 21 points per game on 41 percent shooting.
The Knicks are playing well without Stoudemire, but they have lacked a consistent second scorer -- a role Stoudemire could conceivably fill.
Interim coach Mike Woodson has said that Stoudemire is day to day. Woodson is taking a wait-and-see approach with his star forward.
"I've got to think that the doctors and Amare are on the same page in terms of where he is," Woodson said last week. "When they tell me he's ready to go he'll be right back in the starting lineup, where I expect him to be."
Ian Begley is a regular contributor to ESPNNewYork.com.