Carragher has already announced that he will be retiring from football at the end of the season, although Rodgers believes that the veteran could play next year.
The 35-year-old has become a integral part of Liverpool's defence in recent weeks and the former Swansea City coach has admitted that he will discuss the possibility of keeping him at Anfield next season.
Speaking on Goals on Sunday, Rodgers said: "He's been fantastic and I do [believe he could play next season]. Him and I communicate a lot and he's obviously got something in his mind.
"Him and I 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 in my time there, going in as a manager of a club of that size.
"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 him and I will chat and we'll take it from there."
Carragher has made 33 appearances for the Merseyside club this season.