Thomas Frank's Bees will be ball number four in the draw following our 1-0 Third Round victory over Oxford United at Griffin Park on Saturday; Neal Maupay with the only goal from the penalty spot late on.
The draw will be live on BBC One and will be conducted by former Wolves duo Carl Ikeme and Robbie Keane.
The fourth round is scheduled to take place between Friday 25 January and Monday 28 January.
Winning clubs will receive £180,000 after The FA doubled the prize fund at the beginning of the season.
Ball numbers:
1 BOLTON WANDERERS2 MILLWALL3 GILLINGHAM4 BRENTFORD5 SHEFFIELD WEDNESDAY OR LUTON TOWN6 MANCHESTER UNITED7 EVERTON8 TOTTENHAM HOTSPUR9 DONCASTER ROVERS10 NEWCASTLE UNITED OR BLACKBURN ROVERS11 CHELSEA12 CRYSTAL PALACE13 DERBY COUNTY OR SOUTHAMPTON14 ACCRINGTON STANLEY15 BRISTOL CITY16 NEWPORT COUNTY17 OLDHAM ATHLETIC18 SHREWSBURY TOWN OR STOKE CITY19 ARSENAL20 MANCHESTER CITY21 BRIGHTON & HOVE ALBION22 WEST HAM UNITED23 WATFORD24 BURNLEY25 QUEENS PARK RANGERS26 BARNET27 PORTSMOUTH28 AFC WIMBLEDON29 WEST BROMWICH ALBION30 MIDDLESBROUGH31 WOLVERHAMPTON WANDERERS32 SWANSEA CITY