The 25-year-old right-back has been linked with moves abroad this summer, possibly in part-exchange deals for other City targets.
Richards had a frustrating season in 2012-13, missing the start of the campaign with an ankle problem and then enduring a six-month lay-off after a knee operation.
Richards told the club's website, mcfc.co.uk: "Manchester City is my club and I've never considered playing anywhere else.
"I think there has been speculation because I've got two years left on my contract and Pablo Zabaleta had a fantastic season.
"He's outstanding but that's what you expect at top teams - you expect competition. The season before we won the Premier League and I had a good year but now I'm just happy to be back fit.
"Last season was a bit of a nightmare with injuries. I picked up the ankle problem at the Olympics and came back from that and then tore my cartilage."
Zabaleta excelled in Richards' absence last season and was named as the outstanding right-back in the Barclays Premier League with that spot in the PFA's Team of the Year.
Richards can play at centre-back but has primarily become a full-back and he admits he would be pleased just to rotate with Zabaleta.
He said: "The main thing is to be playing. I know there are a lot of games and I don't expect to play every game but the season we won the title me and Zaba rotated really well together so if we can do that this season I'll be happy."
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- Pablo Zabaleta