City has failed to make an impact in the Champions League two years running and languish 12 points behind bitter rivals Manchester United in the Premier League title race.
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“Only time will tell whether the club decides to sack him or keep him, but he’s doing well," he told the Sun.
“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."
Despite the FA Cup remaining the only likely trophy for Manchester City this campaign, Clichy insists it is too easy to only consider the number of trophies won on a seasonal basis.
“It would be a big disappointment if we don’t win anything because when you taste it, you want it every year," he continued. "But it’s not as simple as that.
“Last season United didn’t win anything and this year they have come back strongly and it looks like they will win something," Clichy insisted.
“One year without a trophy is not a lot. If we don’t win this year, then next season we don’t compete for anything and so on for three or four years then it’s different, but that’s not the case. We need to stay calm.
“Being second and competing for the FA Cup is not too bad. The quality is there and I’m sure there is more to come from this team in years to come.”
Although Manchester United is 12 points clear, Clichy still believes the gap can be closed, as he aims to look at last year's more difficult situation for inspiration.
"We still feel it is similar to the situation we had last year when they were eight points clear with six games to go." Clichy stated.
“That was probably harder than now — 12 points with 12 to go. You can’t feel that you can’t win it at this stage.
“I still don’t think United are better than us. The difference is that when they don’t play well they manage to get the three points whereas when we don’t play well, we lose or get the draw.
“But we still have to go to Old Trafford, that can help. A couple of draws and a defeat for United can change everything."