Carragher says Rooney would be making a big mistake if he left the champions and wasted the chance to work under the former Everton chief again.
He said: “I don’t think Wayne Rooney needs to move on at all. He’s playing for one of the biggest clubs in the world in one of the best leagues in the world.
“The Premier League suits Wayne Rooney and the way he plays the game.
“Just because someone is a top player in the Premier League doesn’t mean he will be a top player in another league.
“It’s not just a manager he doesn’t know that is coming in, it’s a manager he has worked with before, so they both know each other well.
“I know they had problems in the past but I’m sure that has been sorted out now.