Stoudemire underwent surgery March 11 to clean up debris in his right knee. He last played March 7.
At the time of his surgery, the Knicks said Stoudemire was expected to miss four to six weeks.
Stoudemire was asked Tuesday about the possibility of returning in the second round of the playoffs.
"If everything goes great [with rehabilitation], then I'm willing to play," Stoudemire said. "Sooner than later, hopefully, if everything continues to improve."
Stoudemire hopes to begin running full speed by the end of the week. If his knee responds well, he will progress with his rehab.
"Everything's on schedule for the most part. I've got to continue to get stronger, got to get back on the court, start moving around at full speed," Stoudmire said. "... And if I can handle that, then we go up a notch, that's great. Then I'm looking [forward to] hopefully playing soon. We'll see."
Of course, a second-round return for Stoudemire presumes the Knicks advance to the second round. They lead the Boston Celtics 2-0.
"If we continue to win, then that gives me more time to really heal up 100 percent," Stoudemire said. "So that's kind of the blessing that we have right now."
Mike Woodson said Sunday that if Stoudemire returns to the Knicks, he will do so as a member of the regular rotation.
"If he's able to make it back, he will be back in the rotation, ready to play," Woodson said. "I'm expecting him to do what he was doing before he left because he played some pretty good, positive minutes for our ball club before he got hurt."
The Knicks have thrived with Stoudemire out, finishing the regular season 17-6 in their last 23 games and winning the Atlantic Division title for the first time in 19 years. So there is a concern among some that Stoudemire's return could affect the team's chemistry.
Kenyon Martin has emerged as a key contributor in Stoudemire's absence. It's unclear whether Stoudemire's return would affect Martin's minutes.
"Amar'e is going to always be a big piece of our team, that's without a doubt," Woodson said. "He's progressing right along. When he's going to play, I don't know at this point.
"[A healthy Stoudemire] just adds one more good piece, great piece, to the puzzle back out on the floor as we continue this journey," Woodson added.
Stoudemire missed the first two months of the season after undergoing surgery to clean debris from his left knee.
In 29 games, Stoudemire averaged 14.2 points and five rebounds in 23.5 minutes per game. He made 57 percent of his field goals.
Ian Begley is a regular contributor to ESPNNewYork.com.