Defending FA Cup champions Manchester City will visit Newcastle United while Leicester City will host Chelsea in the quarterfinals of the competition.
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Arsenal, who have won the cup a record 13 times, will travel to fellow Premier League side Sheffield United.
Norwich City, which needed penalties to beat Tottenham Hotspur, will welcome the winners of Thursday's clash between Derby County and Manchester United.
The matches will be played across the weekend of March 21-22. The full draw is as follows:
Sheffield United vs. Arsenal
Newcastle United vs. Manchester City
Norwich City vs. Derby County/Manchester United
Leicester City vs. Chelsea