Both semi-finals will be played at Wembley over the weekend of July 18-19, with the final scheduled for Saturday, Aug 1 at the same venue.
Harry Maguire struck an extra-time victor as United saw off 10-man Norwich in the first quarter-final on Saturday, while Chelsea beat Leicester 1-0 on Sunday thanks to Ross Barkley's second-half strike. Arsenal needed an injury-time goal from Dani Ceballos to see them through while Ross Barkley scored the only goal for Chelsea at the King Power Stadium. The Red Devils opened their Premier League campaign with a 4-0 win over Frank Lampard's team before beating them 2-1 in the Carabao Cup in October.
The draw for this year's FA Cup semi-final has been made, throwing up some very tasty ties indeed, including a repeat of the 2016 final.
Arsenal required a stoppage-time effort from Dani Ceballos to book their place in the last four, with the Gunners' victor against Sheffield United coming just four minutes after David McGoldrick had struck a late equaliser.
Manchester City secured their place in the the semi-finals with a 2-0 victory against Newcastle at St James' Park, with Kevin De Bruyne and Raheem Sterling on target.
The two sides faced each other in a Wembley semi-final three years ago, where Arsene Wenger's side managed to prevail over Pep Guardiola before going on to lift the cup. City, meanwhile, have won it six times each.