The 26-year-old has been the subject of one of the biggest transfer stories of the summer after the South American revealed his desire for a change of environment after a controversial end to the season.
Despite the Uruguay international failing to quash speculation linking him with a move to Los Blancos, Carragher, who retired in May, reckons Suárez could still stay at the Merseyside outfit.
“I think he might stay,” said Carragher. “Some big clubs will be interested in him because he is such a top player and that is something we have to accept.
“We can’t complain about that, we bought him off Ajax.
“He signed a contract last summer and he has a few years left and hopefully we can keep him,
“He is very important. He was probably the best player in the Premier League last season and you want to be keeping your best players, which is what he is.”
Suarez, who was nominated for the PFA player of the year award, has scored 51 goals in 96 appearances for the Reds after completing a £22.75m move to Liverpool from Ajax in 2011.