Stoudemire has been sidelined since March 7 with a right knee injury. He underwent a procedure to clean out debris in the knee on March 11.
He has been ruled out of the first two games of the Knicks-Pacers series but may play in Game 3 next Saturday.
Woodson said Stoudemire will scrimmage with his teammates on Thursday. If his knee responds well, he will scrimmage again on Friday.
"If he feels fine after Friday, then I think we will play him Saturday," Woodson said.
Some have expressed concern over how Stoudemire would fit into the Knicks' lineup. New York finished the regular season 17-6 with Stoudemire out and won its first-round series against Boston without him.
Kenyon Martin has emerged as a key contributor in Stoudemire's absence. Woodson has said that Stoudemire's return would not affect Martin's minutes. It's likely that Stoudemire would usurp minutes given to injured sharpshooter Steve Novak.
Woodson said the 6-foot-11 Stoudemire could help the Knicks on the interior against a Pacers team that holds a size advantage over New York.
"If he's right he can help us a lot. There's no doubt," Woodson said.
The Pacers outrebounded the Hawks by a postseason-high 11 rebounds per game in their first-round win. They rebounded a playoff-high 56.3 percent of their misses. So Stoudemire, who averaged five rebounds in 23.5 minutes per game in the regular season, could help Tyson Chandler and Martin in the paint.
A healthy Stoudemire also gives Woodson the opportunity to have multiple big men on the floor simultaneously. The Knicks often featured one big man -- either Chandler or Martin -- at center against the Celtics. Both Chandler and Martin were in foul trouble at different times in the six-game series.
"[Stoudemire] will give us another big man to rotate," Chandler said.
Stoudemire, who did not speak to reporters at Saturday's practice, missed the first two months of the season after undergoing surgery to clean debris from his left knee. In 29 games, he averaged 14.2 points and made 57 percent of his field goals.
Said Woodson: "We will expect the same thing out of him if he comes back."
Meanwhile, star Carmelo Anthony is dealing with pain in his left shoulder but will play in Game 1. Anthony said after the Knicks' Game 6 win on Friday that his left arm "popped in and out" of his shoulder after a collision with Avery Bradley.
On Saturday, he said his shoulder is not dislocated.
"The only time I really feel it is when I extend it hard, get yanked on it, something like that. Other than that I try not to think about it," he said.
Novak will sit out Game 1 with back spasms. He also missed the Knicks' Game 6 win over Boston on Friday.
The Knicks will open their series against Indiana at 3:30 p.m. ET Sunday.
Ian Begley is a frequent contributor to ESPNNewYork.com.