The Uruguay international has made numerous public pronouncements since the end of the season, suggesting a move to Real Madrid interests him and claiming his mistreatment at the hands of the British media has driven him to look elsewhere.
Liverpool have not yet heard from the player or his agent about his intentions and no approach has been made by the Spanish side.
Suarez is still on international duty at the Confederations Cup, where he has a third-place play-off against Italy on Sunday, but once the tournament has finished it is anticipated there will be some movement in regards to his situation.
And despite all the indications pointing towards an exit for the 26-year-old, Carragher, who retired at the end of last season, remains hopeful his former club can hang onto a player who scored 30 goals last season.
"I think he might stay. Some big clubs will be interested in him because he is such a top player and that is something we have to accept," he told ITV.
"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."