Santana, 31, underwent Sept. 14 surgery to repair a torn anterior capsule in his left shoulder.
Two weeks ago, Santana started tossing a baseball every other day.
Alderson said Santana likely will not step onto a mound until about May 1. From that point, it could take six to eight weeks to be ready to contribute.
"So if you do the math, it gets you to the end of June, the middle part of July," Alderson said.
Santana described himself as "optimistic" about his chances to pitch at a high level again. Still, he suffered a rare baseball injury. He could only cite New York Yankees catcher Jorge Posada as another major league player who has undergone the procedure. And he is not a pitcher.
Even Santana is unsure if he will be able to duplicate his pre-shoulder surgery level once healed, although that's the goal.
"When you get your arm all cleaned up and fixed, there's always a question mark, because you never know," Santana said. "Time will tell. But if everything goes right and feels good, I'm going to continue playing as much as I can."
Manager Terry Collins spoke to Santana.
"He said, 'I'm going to be faster than people think,'" Collins said.
Santana said he gets "some tightness" while tossing a baseball, but expressed no concern. Collins said staff members who observed Santana tossing at the Mets' Florida complex this week believe his range of motion is advanced at this point for someone who had undergone shoulder surgery.
"You stretch and it's part of what you're going to go through, I've been told," Santana said about the tightness.
Santana is signed through 2013, at annual salaries of $22.5 million, $24 million and $25.5 million. The club also has an option for 2014 at $25 million, or is responsible for a $5.5 million buyout.
Collins has asked Santana to be outdoors with the team during spring-training workouts to act as a leader, even if he is limited. Santana complied Thursday. However, Santana indicated, he more often likely will stretch with the team and then get to his rehab program independently.
"I don't want to be a distraction," Santana said. "That's for sure."