Tight end Martellus Bennett has been playing with a torn rotator cuff and torn labrum, as first reported by the NFL Network and confirmed by ESPN's Adam Schefter.
Bennett was present at Patriots practice on Friday.
During the Packers' bye week, Bennett said on social media that he was "pretty sure" he would retire after this season. Then he was sidelined with a shoulder injury following the first practice after the bye.
Packers coach Mike McCarthy said Friday that surgery was being discussed before the Packers released Bennett.
"I'm not going to get into the Patriots claiming Marty. I'll just reiterate what I said yesterday: I just know what the facts are and how the timeline came about," McCarthy said. "I talked to him Tuesday [following the bye week] after practice and he [had] a shoulder concern injury. I advised him to get the second opinions. He did that and he went to a number of them.
"The last medical conversation I was involved with in regards to Marty, they were talking about scheduling surgery. After that, then you have the termination and then the claim. I really don't have any comments on that. I've answered the question for the last time, respectfully."
Bennett played for the Patriots in 2016. He had 55 catches for 701 yards and seven touchdowns, playing an integral role in the team's Super Bowl championship season.
The Patriots didn't re-sign Bennett as a free agent in the offseason, electing instead to trade for tight end Dwayne Allen of the Indianapolis Colts. Allen, however, has not recorded a catch in eight games this season; in part because of that, the Patriots' offense has struggled in the red zone.
In claiming Bennett, the Patriots inherit the three-year, $21 million contract he signed with the Packers. If the Patriots don't pick up a $2 million bonus early in the 2018 league year, Bennett would become a free agent again, and the Patriots wouldn't have any commitments on their salary cap, which also likely contributed to the team claiming him.
Information from ESPN Patriots reporter Mike Reiss and ESPN Packers reporter Rob Demovsky was used in this report.