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.
He has reportedly attracted interest at home and abroad but the 25-year-old wants to stay where he is for the remainder of his career.
"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 (full-back)."
Richards made his return in the 5-0 League Cup victory against Wigan Athletic at the end of September and also played the full 90 minutes in the UEFA Champions League defeat to Bayern Munich, and the Premier League triumph at West Ham.