The 22-year-old was linked with clubs such as Liverpool and Juventus in the January transfer window.
But a recent chat about his future with manager Roberto Mancini has persuaded the defender to stay at Eastlands.
“I initiated the contact with Mancini,” said Richards in The People. “I’d had a back injury and then I was on the bench for three games. I wasn’t happy because I was fit, so I went to see him.
“I asked him what was going on because I think I’ve been doing the business this season. He told me to bide my time and then take my chance.
“Mancini makes it easy for you to speak to him. He has a tough side to him but, deep down, he is a soft guy. The chat only lasted about 15 minutes but I’m pleased with how it went.
“Getting a place in the side is tough but Mancini told me that if I concentrated more I could be a top defender and even a world-class defender.
“When a top manager says that, you have to start believing it. I do believe it because when I’m on top of my game I can match anyone.
“It’s about maintaining your confidence. Some of the times I was on the bench were because I was injured but other times it was down to personnel.
“It was frustrating and that’s why I went to see the manager. I want to stay here, of course. There were a couple of links with Chelsea and Aston Villa but I have not heard anything myself.
“I am happy as long as I’m in the team at City but if I’m not playing then I would rather go somewhere else and play.”