The FA Cup semi-final draw threw up a Manchester derby as both United and City overcame their quarter-final opponents.
United beat Arsenal 2-0 on Saturday to make it to the semi-finals and will play City after they beat Reading 1-0 on Sunday.
United are still battling on three fronts as they sit top of the Premier League and welcome Marseille to Old Trafford on Tuesday for the second leg of their Champions League last-16 tie.
City have not won the FA Cup since 1969 and boss Roberto Mancini is under pressure to deliver silverware, having spent heavily in the pursuit of success.
Bolton and Stoke have avoided the Premier League leaders and will face each other for a chance to reach the final after they overcame Birmingham and West Ham respectively.
Bolton's FA Cup drought stretches back even further, to 1958, while Stoke have never reached the final.
Both semi-finals will take place at Wembley on the weekend of April 16-17.