The 3-2 win against Swansea City sent the U's into the fourth round for the first time since the 1998-99 season, when they were paired with Chelsea.
Guus Hiddink's side are one potential giant still in the hat, along with the likes of Manchester City and holders Arsenal.
Midfielder John Lundstram said last week he would love a reunion with former club Everton and for the same reason head coach Michael Appleton's ideal game would be a trip to Old Trafford.
He said: "From a selfish point of view I’d be delighted with that because of my history and I’m still a Manchester United fan, believe it or not.
"I’m sure the chairman would want a big one away.
"I’d be happy with that – the reality is we can’t win this competition but if we keep putting performances in like that we’ll give everyone a lot of entertainment and hopefully make the club a few quid."
The U's will be ball 16 in the draw, which will be made on the One Show from 7.15pm.
Details will be here as soon as United discover their opponents.
Draw numbers in full
2 West Bromwich Albion or Bristol City
3 West Ham United
4 Derby County
5 Exeter City or Liverpool
6 Tottenham Hotspur or Leicester City
7 Colchester United
8 Peterborough United
9 Northampton Town or Milton Keynes Dons
11 Newport County or Blackburn Rovers
12 Ipswich Town or Portsmouth
13 AFC Bournemouth
14 Wycombe Wanderers or Aston Villa
15 Sheffield Wednesday
16 OXFORD UNITED
18 Bury or Bradford City
19 Manchester United
21 Crystal Palace
22 Eastleigh or Bolton Wanderers
23 Nottingham Forest
24 Carlisle United or Yeovil Town
26 Stoke City
27 Leeds United
28 Shrewsbury Town
29 Huddersfield Town or Reading
31 Manchester City
32 Hull City