The 24-year-old has been sidelined since suffering a knee injury that required surgery in City's Premier League win over Swansea last October.
Richards had been in just his fourth match back after missing the start of the campaign with ankle trouble.
The England international has been out longer than hoped, having initially been sidelined until the end of February, but he is now back training with a view to playing at Old Trafford on April 8.
Richards told the club's website: "In the last 10 days, I've been training outside again, doing two days of running and then a recovery day after that.
"I had a big fitness session on Tuesday and I'm starting to feel really good again so, when the lads are back from international duty, I should be taking part in partial sessions with them as I continue to close in on a return.
"I think the Newcastle match will come too soon for me, though I hope to have been training normally by then.
"Realistically, I'm looking more to the game away to United and then the FA Cup semi-final, maybe against United again, to be properly involved again - two relaxing games in a week on the horizon!
"I'll be trying my best to get back into the squad and it will be great just to be back among the lads and getting a feel for everything again."
Manager Roberto Mancini said last week he hoped two other injury victims, Vincent Kompany and Sergio Aguero, would be fit for City's next game against Newcastle on March 30.
Captain Kompany has not played since suffering a calf injury in the FA Cup fourth-round win at Stoke on January 26.
He could actually return to action before that in Belgium's World Cup qualifier in Macedonia on Friday or the return fixture against the same opponents in Brussels next Tuesday.
Belgium assistant coach Vidal Borkelmans told Sky Sports News: "Vincent is very important, he is captain of the team.
"We are quite happy he has been here. We will see. We will make about Wednesday a point whether he plays or not.
"He must listen to the body. He must say, 'I am okay' and then it is a decision of the coach what he does, yes or no."
Aguero has missed the last three games with a knee injury and has been back in his native Argentina receiving treatment.
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