Manager Joe Royle, after hearing the draw on Sunday, said: "No disrespect to Morecambe, and we will not take them lightly, but this is a game we should win.
"It is the second biggest game for them for years, the first was a couple of years ago at home.
"We are happy to get a home draw, but having said that our away form has been better."
Full Draw:
Leicester v Bristol City
Scunthorpe or Carlisle v Leeds
Gillingham v Sheff Wed
Chelsea v Middlesbrough
Ipswich v Morecambe
Preston v Bristol Rovers or Rochdale
Man City v Liverpool
Shrewsbury v Everton
Southend or Bournemouth v Crewe
Plymouth v Dagenham & Redbridge
Cambridge or Northampton v Millwall
Bolton v Sunderland
Darlington v Farnborough
Walsall v Reading
Fulham v Birmingham
Stoke v Wigan
West Ham v Nottm Forest
Charlton v Exeter
Sheffield United v Cheltenham
Aston Villa v Blackburn
Cardiff v Coventry City
Wolves v Newcastle United
Southampton v Spurs
Norwich v Brighton
Arsenal v Oxford United
Grimsby Town v Burnley
West Brom v Bradford City
Rotherham v Wimbledon
Brentford v Derby County
Blackpool v Crystal Palace
Manchester United v Portsmouth
Macclesfield Town v Watford
Ties to be played over the weekend of 4 January and 5 January.