Suarez had told friends he was considering quitting Anfield in the wake of the scandal, and even talked up a move to Paris St Germain, but appears to have changed his mind.
Carragher said: "It's vitally important he stays. I see no reason why he would want to leave.
"He is playing well and scored his most important goal for us. I thought he was brilliant. Our best player. I wouldn't swap him for anyone in the league. He is a fantastic player and hopefully he will take that forward into the cup final."