The 35-year-old announced earlier this season that this campaign would be his last in the Premier League, but Rodgers is hoping to persuade him otherwise.
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The Liverpool legend had been tipped to venture into a coaching role at the club, but Rodgers thinks Carragher still has more to offer on the pitch.
"Carra’s been fantastic and I do believe he could play next season," Rodgers told Sky Sports' Goals on Sunday. "He and I communicate a lot and he’s obviously got something in his mind.
"We will sit down between now and the end of the season anyway and we’ll see where it goes. If he does go, I will certainly miss him because he’s been brilliant for me.
"He’s shown great respect and really helped me and the other guys.
"The thing for now is to keep performing the way he is until the end of the season and between then and now he and we will chat.
"This guy’s incredible. I want to put that on record."