Richards, who were once linked with the likes of Manchester United and Chelsea, has been linked with a £5million move to either Wigan or Bolton.
He told his personal website: “I was shocked to wake up and read in the newspapers that I have been linked with a move away from City, with speculation suggesting I could move to Wigan or Bolton in a £5 million deal.
“These rumours are the first I’ve heard about it, and they’re utterly ludicrous. I’m as happy as happy comes at Manchester City, and I feel the club is now moving in the same direction I knew it would.
“On a personal level, playing for Manchester City can take me to next level, and I hope to stay here and win things.”