The Hammers progressed through to the fifth round with wins over Stockport and Doncaster, while the hosts overcame Championship Watford and rivals Liverpool to progress this far.
David Moyes' side saw the remarkable winning run that has propelled them into the Premier League top-four conversation ended by Liverpool last week, but bounced back with a win over Aston Villa before being held to a goalless draw by Fulham at the weekend.
Man United, meanwhile, currently remain Manchester City's closest challengers in the title race, thrashing sorry Southampton 9-0 but crucially dropping points against Sheffield United, Arsenal and Everton.
Only Arsenal (14) have won more FA Cups than the Red Devils (12), with the latter's last triumph coming back in 2016. They lost in the final two years later.
The last of West Ham's three triumphs was 41 years ago, while they haven't reached the final since 2006.
Date, kick-off time and venue
Manchester United vs West Ham is scheduled for a 7:30pm GMT kick-off on Tuesday, February 9, 2021.
The match will be played behind closed doors at Old Trafford due to ongoing coronavirus restrictions.
How to watch Man Utd vs West Ham for free
TV channel: The match will be televised on BBC One for those with a valid TV licence, with coverage from 7pm.
Live stream: The contest can also be viewed online via the BBC Sport website or BBC iPlayer.
Man Utd vs West Ham team news
Man United will be without Paul Pogba against West Ham and for the next few weeks due to a thigh injury that forced him off in the first half of Saturday's 3-3 draw at Everton.
Eric Bailly is training again after injury, but Ole Gunnar Solskjaer does not expect him to be involved on Tuesday.
Phil Jones is also still working his way back following summer knee surgery.
West Ham could be without their sole senior striker in Michail Antonio, who is fatigued and may miss out after being substituted as a precaution against Fulham.
Moyes will make a final decision on the influential 30-year-old before the game.
Soucek is available after his controversial red card was overturned, but Arthur Masuaku is still around a month away from returning following knee surgery.
Manchester United loanee Jesse Lingard is cup-tied and would not have been eligible to face his parent club regardless.
Man Utd vs West Ham prediction: 2-1 home win
This is a tough contest to call. Bar that blip against Liverpool, West Ham's form in 2021 has been nothing short of remarkable and a trip to Old Trafford will hold no fears for a side that have won exactly half of their away matches in the League this term, losing only three.
They will also want to seek revenge for that 3-1 comeback defeat suffered at the London Stadium in early December. Man United are a quality outfit when things are clicking, but they remain prone to defensive errors as we recently witnessed at home against both Sheffield United and Everton.
If they can limit those mistakes, the hosts should prevail - especially if Antonio misses out for the Hammers.
Head to head (h2h) history and results
Man Utd wins: 67
West Ham wins: 45
Last meeting: West Ham 1-3 Manchester United (05/12/2020)
Man Utd vs West Ham betting odds and tips
Man Utd to qualify: 1/3
West Ham to qualify: Between 5/2 and 13/5
Man Utd to win 2/1: 17/2
Odds via Betfair Exchange (subject to change). Click here to find out more.