NFL free agency has been open for several weeks, but for former Giant Will Beatty it begins on Monday. That’s when the offensive lineman who was cut by the Giants earlier this offseason expects to get the green light from doctors in New York following surgery on his right shoulder. Teams have expressed interest in him since he was released — the Raiders and Broncos both reached out and asked him to visit for a workout — but he decided to decline those invites until he is fully healed.

“I want to make sure I can perform and show who I really am,” Beatty told Newsday on Tuesday from his home in Arizona. “I don’t want to show them an injured Will. I don’t want to visit a team and say ‘It’ll get better.’ I want to be good and ready to go. I want to say ‘I’m ready and I can be your guy.’ ”

That strategy could be a bit of a gamble. While Beatty has been rehabbing, other free-agent linemen have been signing. The Broncos and Raiders, the teams that sniffed around Beatty, both signed players to play left tackle for them next season. There are only a handful of teams currently looking for a starter at that position (which Beatty believes he can be, although he said he is willing to play other positions as well). The Giants are looking for a veteran lineman, but a reunion is unlikely given the abruptness of the divorce.

Things change quickly in the NFL, however, and injuries or other situations could create sudden opportunities. Beatty hopes to be ready for those.

Beatty missed all of the 2015 season with a torn pectoral suffered in the spring and the shoulder injury that prevented him from returning from short-term IR. But when he was last on the field, in 2014, he played well and was the Giants’ most consistent lineman. He said he thinks he can return to that form, and that missing last year has only increased his hunger to play and play well.

“I’m going to be great this season,” he said with the kind of confidence he rarely expressed during his Giants tenure. “I’m ready to go. This will be a new start for me, a new chance for me. I don’t want to miss any of it.”

Doctors have told him once he is cleared, he should not have any concerns about reinjuring the shoulder. That’s one of the reasons why he has been so deliberate in his rehab. He doesn’t want any setbacks before he gets to the finish line.

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“I’m trying to push the envelope without tearing the envelope,” he said of his pace.

Despite speculation that his days with the Giants were numbered — many saw his large salary-cap hit for 2016 and the emergence of rookie Ereck Flowers as his replacement in 2015 as signs of the end — Beatty, 31, said he was surprised when the team released him.

“I was not expecting that,” he said. “After seven years in the NFL, I still don’t understand general managers and coaches and stuff like that.”

He said the hardest part about being released was that he was still rehabbing his shoulder.

“I couldn’t prove that they are missing out on something,” he said.

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After Monday, he’ll likely get that chance. Somewhere.