The defender, who recently returned to action following a hamstring injury, joined City in 2005 and has since made over 200 appearances for the club.
Richards has reportedly attracted interest at home and abroad but the 25-year-old wants to stay where he is for the foreseeable future.
"I'm not leaving City," Richards told The Sun. "It's my club and I love it here. Ten more years - that's my aim.
"I am back fit now and believe when I'm fit I'm as good as anyone in the division playing that role [fullback]."
Richards made his return in the 5-0 Capital One Cup victory against Wigan in September and also played the full 90 minutes of the Champions League defeat to Bayern Munich, and the Premier League triumph at West Ham.