Manchester City will face Chelsea in the semi-finals of the FA Cup while Leicester will meet Southampton.
Chelsea reached the last four with victory over Sheffield United while City beat Everton and Southampton saw off Bournemouth.
Leicester and Manchester United were level at 1-1 at half-time of their quarter-final when the draw for the semi-finals was made, but the Foxes scored twice in the second half to reach their first semi-final since 1982.
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The semi-finals will be played on the weekend of 17 and 18 April at Wembley.
It has been reported that one of the matches is being considered as a pilot event in government plans to return fans safely to stadiums while it is expected that the FA Cup final in May will be played in front of 20,000 fans.
Arsenal won the FA Cup last season but were eliminated in the fourth round by Southampton this season.
Man City have only won the competition once in the last 10 years - in 2019 - and are aiming to secure it this season as part of a quadruple.
They look set to win the Premier League title and are in the final of the Carabao Cup and quarter-finals of the Champions League.
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