Stoudmemire has been out since March 24 with a bulging disk in his lower back.
Woodson said before Tuesday's game against the Boston Celtics that Stoudemire could "possibly" play Friday, depending on how he feels after practice on Thursday.
Stoudemire will not play on Tuesday against Boston or Wednesday at New Jersey.
"Thursday, we'll have another practice to kind of see where he is. And if everything goes well in that practice then there's possibility (that Stoudemire could return Friday)," Woodson said.
The coach added that Stoudemire would be inserted into the starting lineup upon his return. Carmelo Anthony had been starting at power forward in place of Stoudemire. Woodson has said that Anthony will move back to small forward when Stoudemire returns. It is unclear who will be removed from the starting five, but Landry Fields, who has been struggling of late, is a possible candidate.
"That's something that, you know, I have a few days to think about," Woodson said. "But whoever goes to the bench, he's got to come off the bench and give productive minutes so that's how I look at it."
Woodson said Stoudemire has not been cleared by team doctors but has responded well to contact during recent scrimmages, an important hurdle in his return to the court.
"He's been going against (Knicks forward/center) Josh Harrellson and Josh has been banging him pretty good. So we'll see," Woodson said.
Stoudemire scrimmaged with teammates during the team's off-day on Monday and practiced for the first time last Saturday.
He had previously been working out and shooting before games with assistant coach Kenny Atkinson.
Some observers thought that Stoudemire may come off the bench upon his return to the lineup, both to give the second unit a boost and to keep he and Anthony from sharing the floor. Stoudemire's statistics from this season indicate that he is less productive when playing with Anthony.
But Woodson stated emphatically that Stoudemire would return to the starting lineup, when he is healthy enough to play.
"I've got to make it work," he said of the Anthony-Stoudemire pairing.
The Knicks are 7-4 without Stoudemire entering Tuesday's game, but they have lacked a consistent second scorer -- a role Stoudemire could conceivably fill.
Stoudemire was shooting around 40 percent from the field and averaging 17 points -- well below his career averages. But before he went down with the back ailment, Stoudemire seemed to be turning a corner, averaging 18 points on 57 percent shooting in the five games before his injury.
Stoudemire hasn't talked about his injury to reporters since he first suffered it on March 24. He didn't want to talk about a potential return date prior to Tuesday's game but did say that he'd "be back soon."
"I definitely have to get some games under my belt before the playoffs," Stoudemire said.
Ian Begley is a regular contributor to ESPNNewYork.com.