"They kind of just said, 'Thanks for everything,' at the end of the year and I haven't heard from them since," Carter told CSNNE.com on Tuesday. "But I'm optimistic everything works out."
Carter played 14 games for the Patriots in 2011, before a quadriceps tear in the Week 14 matchup with Denver ended his season prematurely. At the time, he had a team-leading 10 sacks.
The 32-year-old said he's been rehabbing two to three hours per day six days a week in hopes of landing another gig with New England, according to the report.
"I could not have enjoyed that season any more than I did," Carter said. "I was working with guys who just love the game of football, the Patriots organization does things the right way, the city was awesome — people wanted to know the players whether they were stars or not. It was such an amazing experience I'd love to experience it again.
"It is a goal to win it all and I understand the journey starts in the offseason. Hopefully I get a chance to try again."