Steve Perryman, Exeter’s director of football, said: "All our supporters are going to love this tie and love travelling up there."
The tie will be played at Old Trafford on Saturday 8 or Sunday 9 January 2005 with a fairly safe bet that United's game will be televised.
FA Cup Third Round Draw in full
Arsenal v Stoke
Swindon/Notts Co v Middlesbrough
Man Utd v Exeter
Plymouth v Everton
Leicester v Blackpool
Derby v Wigan
Sunderland v Crystal Palace
Wolves v Millwall
Yeading v Newcastle
Hull v Colchester
Tottenham v Brighton
Reading v Stockport/Swansea
Birmingham v Leeds
Hartlepool v Boston
Milton Keynes Dons v Peterborough
Oldham v Man City
Chelsea v Scunthorpe
Cardiff v Blackburn
Charlton v Rochdale
West Ham v Norwich
Sheff Utd v Aston Villa
Preston v West Brom
Rotherham v Yeovil
Burnley v Liverpool
Bournemouth v Chester
Coventry v Crewe
Watford v Fulham
Ipswich v Bolton
Portsmouth v Gillingham
Northampton v Southampton
QPR v Nottm Forest
Luton v Hinckley/Brentford