The draw for the fourth round of the FA Cup will take place on Sunday 12 January.
It will follow the televised Arsenal v Manchester United tie that afternoon, which kicks off at 3pm.
Following the conclusion of the game at Emirates Stadium, the draw will be broadcast live on BBC One, while Brentford's fourth-round opponents will also be confirmed on the club's social media channels and website.
The Bees, who defeated Championship side Plymouth Argyle X-X in the third round on Saturday afternoon at Gtech Community Stadium, will be ball number 21.
Fourth-round ties will take place on the weekend of 8/9 February.
Ball numbers
1 Southampton or Swansea City
2 Arsenal or Manchester United
3 Exeter City or Oxford United
4 Leyton Orient or Derby County
5 Reading or Burnley
6 Aston Villa or West Ham United
7 Norwich City or Brighton & Hove Albion
8 Manchester City or Salford City
9 Millwall or Dagenham & Redbridge
10 Liverpool or Accrington Stanley
11 Bristol City or Wolverhampton Wanderers
12 Preston North End or Charlton Athletic
13 Chelsea or Morecambe
14 Middlesbrough or Blackburn Rovers
15 AFC Bournemouth or West Bromwich Albion
16 Mansfield Town or Wigan Athletic
17 Tamworth or Tottenham Hotspur
18 Hull City or Doncaster Rovers
19 Sunderland or Stoke City
20 Leicester City or Queens Park Rangers
21 Brentford or Plymouth Argyle
22 Coventry City or Sheffield Wednesday
23 Newcastle United or Bromley
24 Everton
25 Wycombe Wanderers or Portsmouth
26 Birmingham City or Lincoln City
27 Leeds United or Harrogate Town
28 Nottingham Forest or Luton Town
29 Cardiff City
30 Ipswich Town or Bristol Rovers
31 Fulham
32 Crystal Palace or Stockport County