The 24-year-old has been out since October and has only appeared four times for City all season.
Mancini has revealed that Richards has been training well but is not yet ready to play.
"This is strange, I don't know how it is possible," Mancini told ESPN. "I hope that in maybe three of four weeks he'll be ready.
"His knee was not 100%, he continues to work and now he has been working for two months.
"From when he starts work with the team he needs another two weeks. I hope maybe he can start with the team next week."
City are currently facing Barnsley in the FA Cup quarter-final.