The draw will take place live on BBC One from Stamford Bridge at 7:30pm.
It will be hosted by Mark Chapman who will be assisted by Balon d’Or winner Ruud Gullit and former England international Paul Ince.
The Bees will be ball 59 following their 1-0 win over Stockport County on Sunday.
The Third Round stage sees sides from the Championship and Premier League enter proceedings for the first time and this is the furthest Barnet have gone in the competition since the 2007/08 season.
Ball Numbers:
1 – AFC Bournemouth
2 – Arsenal
3 – Aston Villa
4 – Birmingham City
5 – Blackburn Rovers
6 – Bolton Wanderers
7 – Brentford
8 – Brighton & Hove Albion
9 – Bristol City
10 – Burnley
11 – Cardiff City
12 – Chelsea
13 – Crystal Palace
14 – Derby County
15 – Everton
16 – Fulham
17 – Huddersfield Town
18 – Hull City
19 – Ipswich Town
20 – Leeds United
21 – Leicester City
22 – Liverpool
23 – Manchester City
24 – Manchester United
25 – Middlesbrough
26 – Millwall
27 – Newcastle United
28 – Norwich City
29 – Nottingham Forest
30 – Preston North End
31 – Queens Park Rangers
32 – Reading
33 – Rotherham United
34 – Sheffield United
35 – Sheffield Wednesday
36 – Southampton
37 – Stoke City
38 – Swansea City
39 – Tottenham Hotspur
40 – Watford
41 – West Bromwich Albion
42 – West Ham United
43 – Wigan Athletic
44 – Wolverhampton Wanderers
45 – Guiseley or Fleetwood Town
46 – Luton Town
47 – Wrexham or Newport County
48 – Tranmere Rovers or Southport
49 – Barnsley
50 – Shrewsbury Town
51 – Solihull Moors or Blackpool
52 – Grimsby Town
53 – Peterborough United or Bradford City
54 – Woking
55 – Oldham Athletic
56 – Lincoln City
57 – AFC Wimbledon
58 – Oxford United
59 – Barnet
60 – Portsmouth
61 – Walsall or Sunderland
62 – Accrington Stanley
63 – Doncaster Rovers
64 – Gillingham
