Russell Slade's side are currently sixth in the Championship League table.
The last time the two sides met was during the 1984/85 season when the Mariners won 4-2 at Cardiff and then had a 6-3 victory at Blundell Park.
The ties will be played between the 8th and 11th of January.
The draw in full:
Watford v Newcastle United
West Bromwich Albion v Bristol City
West Ham United v Wolverhampton Wanderers
Salford City or Hartlepool United v Derby County
Exeter City v Liverpool
Tottenham Hotspur v Leicester City
Colchester United v Charlton Athletic
Peterborough United v Preston North End
Northampton Town v MK Dons
Arsenal v Sunderland
Newport County v Blackburn Rovers
Ipswich Town v Portsmouth
Birmingham City v AFC Bournemouth
Wycombe Wanderers v Aston Villa
Sheffield Wednesday v Fulham
Oxford United v Swansea City
Brentford v Chesterfield or Walsall
Bury v Bradford City
Manchester United v SHeffield United
Everton v Dagenham & Redbridge or Whitehawk
Southampton v Crystal Palace
Eastleigh v Bolton Wanderers
Nottingham Forest v QPR
Carlisle United v Yeovil Town
Chelsea v Leyton Orient or Scunthorpe United
Doncaster Rovers v Stoke City
Leeds United v Rotherham United
Cardiff City v Grimsby Town or Shrewsbury Town
Huddersfield Town v Reading
Middlesbrough v Burnley
Norwich City v Manchester City
Hull City v Brighton & Hove Albion