Richards only made seven Premier League appearances for City last season as injury problems wrecked his campaign, allowing team-mate Zabaleta to establish himself in the team.
Transfer speculation surrounded Richards for the early part of the summer, with Serie A and rival Premier League clubs said to be competing for his signature.
However, last month, City chairman Khaldoon Al Mubarak confirmed that the club are ready to open talks with the defender's advisors over a new contract.
The 25-year-old has already gone on the record as saying he would like to stay at the Etihad for the rest of his career, but he wants to win the trust of new coach Manuel Pellegrini before he puts pen to paper again.
"I've got two years left on my contract and Zabaleta had a fantastic season," said Richards.
"He's outstanding, but that's what you expect at top teams. You expect competition. The season before, we won the league and I had a good season. Now I'm just happy to be back fit.
"It's nice to hear what the chairman said because I've been here since I was 14. I probably know the club better than anyone out of the players. But 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 league, me and Zaba rotated really well together. If we can do that this season, I'll be happy."
Richards, who is with City in Hong Kong for the Barclays Asia Trophy tournament, is now looking to impress Pellegrini and thus secure his future.
"The manager has come in and I want to see his ideas and what he can do," he added to reporters.
"I want to be here and I don't know why any player would want to leave, but every player wants to play football. If I can do that here, it's perfect."