Chelsea will face Luton Town in the FA Cup fifth round while Liverpool will welcome Norwich City after they beat Cardiff City on Sunday.
Manchester City, who won the competition in 2019, face a trip to Peterborough United and Middlesbrough's reward for beating Manchester United is a visit from Tottenham Hotspur.
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Boreham Wood, the lowest-ranked side left in the competition, could face Frank Lampard's Everton if they overcome Championship side Bournemouth on Sunday.
Holders Leicester City must still overcome Midlands rivals Nottingham Forest and will face Huddersfield Town in the fifth round with a win.
Southampton vs. West Ham United, who narrowly beat National League Kidderminster Harriers on Saturday, and Liverpool vs. Norwich are the only all-Premier League ties in the fifth round.
Crystal Palace, managed by four-time FA Cup-winner Patrick Vieira, welcome Stoke City.
Ties will be played on Wednesday March 5 to minimise disruption to league fixtures.
FA Cup fifth-round draw
Luton Town vs. Chelsea
Crystal Palace vs. Stoke City
Peterborough United vs. Manchester City
Liverpool or Cardiff City vs. Norwich City
Southampton vs. West Ham United
Middlesbrough vs. Tottenham Hotspur
Nottingham Forest or Leicester City vs. Huddersfield Town
Everton vs. Bournemouth or AFC Boreham Wood