The ex-Liverpool boss isn't a popular choice amongst Blues fans.
But Redknapp insisted to The Sun: "I know Benitez isn't a popular choice, but the ball's in his court.
"I have always said the punters do not really care who's in charge, so long as the team is winning and the points are racking up. You could have Saddam Hussein in charge of your club and if results went well they would be chanting his name.
"So Rafa has to start by beating City - if he manages that, it'll be a different story."