Town would face one of three if they beat TranmereThe FA Youth Cup Third Round Round draw was made at Wembley Stadium on Friday morning.
Should Shrewsbury Town beat Tranmere Rovers away in the Second Round Proper, they would face a trip to either Mansfield Town, Knaresborough Town or Northampton Town in the Third Round of the competition.
Knaresborough host Northampton in the First Round Proper hoping for the right to face Mansfield away in the Second Round Proper.
Ian Dawes' side won 7-0 against Lincoln City at the Greenhous Meadow on Tuesday night in the First Round Proper.
The date, time and venue for Shrewsbury's clash against Tranmere will be confirmed in due course, although the tie will be played no later than Saturday 22 November.
The full Third Round draw is as follows:
Mansfield Town or Knaresborough Town or Northampton Town v Tranmere Rovers or Shrewsbury Town
Colchester United or Cheltenham Town v Ipswich Town
Nottingham Forest v Newport County or Milton Keynes Dons
Leicester City v Wigan Athletic
Oxford City or Luton Town v Royston Town or Potters Bar Town or Welling United
Arsenal v Reading
Huddersfield Town v Crystal Palace
Brighton & Hove Albion v Derby County
Dartford or Thamesmead Town or Portsmouth v Bolton Wanderers
Burton Albion or Kidderminster Harriers v Blackpool
Tottenham Hotspur v Blackburn Rovers
Sunderland v Fleetwood Town or Sheffield United
Leeds United v Chelsea
Gillingham or AFC Wimbledon v Burnley
Southampton v West Ham United
Stevenage or Needham Market or Wealdstone v Everton
Doncaster Rovers or Peterborough United or Notts County v Norwich City
Birmingham City v Queens Park Rangers
AFC Bournemouth v Rochdale or Coventry City
Liverpool v Bradford City or Barnsley
Millwall v Newcastle United
Manchester City v Oxford United or Swindon Town
Rotherham United v Wolverhampton Wanderers
Southend United or Leverstock Green or Barnet v Middlesbrough
Manchester United v Ellesmere Rangers or Port Vale or Bury
Swansea City v Watford
Crewe Alexandra or Abbey Hey or York City v Fulham
Sheffield Wednesday v Stoke City
Hull City v Brentford
West Bromwich Albion v Maidenhead United or Poole Town or Torquay United
AFC Fylde or Chesterfield v Aston Villa
Charlton Athletic v Cardiff City
All 32 ties will be played by Saturday 20 December 2014.
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