The Uruguay international has been angling for a switch to Real Madrid after claiming that the treatment that he has received from the British media has caused him to consider a move away from England.
"I think he might stay," Carragher told ITV Sport. "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."
Reports have claimed that the Reds will want £40m for Suarez if they are forced to relinquish the frontman this summer.