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Clichy has signed a four-year deal with the Eastlands outfit after completing a £7million switch from Arsenal.
"There is no limit," he told www.mcfc.co.uk. "Of course, you have to be realistic but where they have come from in three years is phenomenal. And I want to win things."
He added: "The Champions League is going to be difficult because it is the first time for Manchester City.
"The Premier League is important for the fans and shows who has been the best team during the whole season.
"The FA Cup has been done last year. Hopefully we can repeat it. The Carling Cup is the least important but it is still a trophy.
"We will go for everything and see what we get at the end of the season."
Compared to Cesc Fabregas and Samir Nasri, who is also on City's wanted list and has been tipped to be reunited quickly with Roberto Mancini's first summer signing, Clichy may not be quite as important to most Gunners fans.
However, if the star duo also quit, big questions will be asked of the Londoners' future direction.
"We started well and collapsed at the end of the season after the (Carling Cup) final," reflected Clichy on another barren campaign at the Emirates. "These things happen in football. That is why you can see the importance of having a big squad. Sometimes it is difficult to have a lot of players because you have to leave some out. But you need to have a big squad to go all the way."
Source: PA
Source: PA