Boro will play Manchester United or Exeter City away on the weekend of the 29/30th January.
The full draw is as follows:
Derby v Watford or Fulham
Man Utd v Exeter v Middlesbrough
Cardiff or Blackburn v Colchester
Chelsea v Birmingham
West Ham v Sheff Utd
Oldham v Bolton
Arsenal v Wolverhampton
Everton v Sunderland
Nottm Forest v Peterborough
Brentford v Hartlepool or Boston
Reading or Swansea v Leicester or Blackpool
Burnley or Liverpool v Bournemouth
Southampton v Portsmouth
West Brom v Tottenham
Newcastle v Coventry
Charlton v Yeovil