The 34-year-old has played more than 700 games for the club he joined as a schoolboy, including over 500 in the Premier League, but his contract expires next summer and it appears increasingly unlikely that he will be offered a new deal.
"There is a chance that I will retire at the end of the season," Carragher told the Daily Express. "It is the last season of my contract and the club have not said anything to me yet.
"I am open-minded, but I would not play on if I was killing the team when I played. I would not be hanging on for money or anything.
"And I would not go anywhere else. It is Liverpool or nothing for me."