Rodgers has admitted Carragher was one of the players he sought opinions from when he took over from Kenny Dalglish in June.
But for now the Reds boss wants to get the best out of what remains of the defender's career.
"Jamie has been absolutely outstanding for me since I joined the club," he said. "He has been a model professional on and off the pitch and has shown an unswerving commitment to our work.
"We still have a lot to play for as we look to finish as high up the Barclays Premier League as possible and continue our progression in the Europa League, a competition we'd like to win.
"He will have a significant role to play for us between now and May, and I know his commitment and dedication on the pitch will remain as it has done his entire career at Liverpool.
"When the time is right we, as a team and a club, will give the man the tribute and recognition he deserves; I know the supporters will want to say thank you to someone who has served them with such distinction for so long."