Chris Cooley, the Redskins’ franchise leader in receptions by a tight end, was released by the team before this season. (John McDonnell/The Washington Post)

Veteran tight end Chris Cooley has agreed to rejoin the Washington Redskins, a person familiar with the situation said Sunday night.

Cooley is scheduled to undergo a physical Monday and his re-signing will become official after that, the person said, speaking on the condition of anonymity because the team had made no official announcement.

“It’s going to happen,” the person said.

Cooley rejoins the Redskins after tight end Fred Davis’s season was ended when he suffered a torn left Achilles’ tendon during Sunday’s loss to the New York Giants.

Cooley declined to comment when reached Sunday night, saying it would be premature but he would address the issue as soon as he could.

The Redskins released Cooley, their career leader in catches by a tight end, before the season but left open the possibility of re-signing him, particularly if they were to suffer an injury at the position.

Update, 11:10 p.m.: Cooley drew interest from other NFL teams while he was a free agent but wasn’t interested in signing a minimum-salary contract elsewhere. He said recently that he would like to return to the Redskins if the team wanted him. He did a bit of broadcasting work and visited the locker room at Redskins Park in recent weeks.

“I don’t know what’s going to happen,” Cooley said during an interview last month. “I want to play here, but I don’t know if anything will happen with that.”

Cooley said then that it probably would take an injury to Davis or backup tight end Niles Paul for the Redskins to be interested in re-signing him.

“The way it looks to me is if something happens here, they would love to have me,” Cooley said at the time. “If Fred gets hurt or something like that, I think I’d be the guy they sign. I think that.”

That interview came after Cooley had met with Redskins General Manager Bruce Allen.

Cooley also said during the interview: “If they call me at some point this season, that’s great. If they don’t, that’s fine too. I’m not going to worry about it too much. I’m happy with what I’ve done here. I’m satisfied with my career. If I don’t play again, that’s how it is. I’ll go through the season and see what the offers are. I’ll go through free agency and see if there’s interest. If I’m not playing at that point, I’ll see about whether to retire or not.”

Cooley knows the offense and already has worked with rookie quarterback Robert Griffin III in offseason practices and in training camp.

Cooley, 30, has 428 catches in eight seasons with the Redskins. He is a two-time Pro Bowl selection and had a 77-catch season as recently as two years ago. But he had only eight catches in five games last season before being placed on the injured reserve list with finger and knee injuries.

He said during training camp that his ailing knee was feeling better. But much of the playing time that he received during the preseason was at fullback, not tight end, and the Redskins opted to let him go and open the season with Paul and Logan Paulsen backing up Davis at tight end.