Clichy believes Mancini should be given more time after two trophies in the previous two years.
He told The Sun: "Only time will tell whether the club decides to sack him or keep him, but he's doing well. It's the people above who decide - but I believe he can take us higher.
"He's the one who brought me here. Of course I'd like to see him stay. As a player you want to give your best for a manager like him.
"If you look at his record, he's the one who brought silverware to this club, the FA Cup, Community Shield, Premier League. You have to give credit where it's due.
"I think people say with that money any manager could do the job but I doubt it."