Amar’e Stoudemire is ramping up his workouts and says he could play in the Knicks’ final two preseason games and the season opener against Milwaukee Oct. 30.

After flying through his most strenuous workout Tuesday, Stoudemire came into the press room, sweating profusely and exuding optimism he didn’t show on Media Day nine days ago.

Stoudemire went through a host of solitary basketball drills and did his usual training-room workouts — running in the pool and using an exercise machine.

“It’s going great,’’ Stoudemire said. “I couldn’t be more pleased with the progress right now. I’m still getting stronger, still getting strong enough to withstand the pressure of playing. The progress has been great so far.’’

Stoudemire hasn’t been cleared to scrimmage yet or run on the court at full speed. Until Tuesday, it had seemed a long shot he could be ready for the season opener. And the Knicks didn’t seem to mind. After Stoudemire underwent a minor knee procedure in July, they kept him from rehabbing aggressively until training camp.

But now Stoudemire, who played just 29 regular-season games last season, is making a big push. His mood seemed much brighter than at any point during training camp where he mostly has been out of sight. He expects to be cleared to run at full speed next week.

“It’s definitely a possibility,’’ Stoudemire said of playing in the opener. “It’s matter of how strong my legs are. I’m working my butt off to gain strength. Hopefully I’ll be ready by the season opener.

“Everyone knows when I’m healthy, what kind of player I am and what I bring to the table.’’

The Knicks open the preseason Wednesday in Providence against the Celtics to begin a three-game trip. They have seven preseason games and Stoudemire wants to play in the final two.

“That’s a possibility for sure,’’ Stoudemire said. “If everything keeps progressing the way it has been, there’s a lot of great news how I felt. If that continues, I look forward to playing before the preseason is up.’’

Stoudemire wouldn’t identify the procedure he had in July, but said it wasn’t nearly as invasive as the two knee debridement surgeries he underwent last season.

He won’t make the first trip to Providence, Toronto and Manchester, N.H.

“Traveling these first [three] games is not very important,’’ Stoudemire said. “The most important thing is to stay here on a consistent basis to train in the comfort zone of the training center with the training staff and when guys come back I should be a step further than when I left.’’

Carmelo Anthony said Stoudemire’s recent injury history was “sad’’ and admitted it was bittersweet since he came to the Knicks because of Amar’e.

“I think about it sometimes,’’ Anthony said. “He was one of the reasons I wanted to come to New York. Me never having that chance to have a full season [with him] and get a rhythm going with him, it’s not something I thought would happen.

“I know it’s taken a toll on him mentally and emotionally. As a friend. it’s hard for me to sit back and act like it doesn’t bother me. I know how much hard work he’s put into training and rehabbing. To go forward and take steps back, it’s sad.’’

However, Stoudemire’s demeanor Tuesday brightened Anthony’s outlook.

“Right now it seems like he’s in a very good mood,” Anthony said. “I would love to see him start back up for us at the start of the season. It’s another weapon we need. We could’ve used him last season at certain points. To get a fresh start to this season, we need him.’’

Coach Mike Woodson said the possibility of Stoudemire playing in opener is back on the radar. The Knicks will have him on a minutes restriction — likely at 20.

“He hasn’t had any setbacks, which is nice,’’ Woodson said. “I’m hoping he plays some [in preseason]. You have to gauge it and see. If he can play 10 minutes a game in the exhibition season, we’ll play him. That’s providing he doesn’t have any setbacks and continues the pace he’s on.’’