The Clarets will launch their FA Youth Cup bid with a home tie against either Oxford United or Barnet.
Burnley enter the competition at the third-round stage and will find out their opponents when Oxford and Barnet meet in round two on Wednesday, 14 November.
Oxford started their run in the competition with a 3-0 win at Hemel Hempstead in round one, while National League side Barnet have beaten Peterborough Sports, Bishops Stortford and Boreham Wood to get this far.
The Clarets beat Leeds United in the third round last season but then lost to Plymouth Argyle at Turf Moor in the last 32.
Third-round ties must be played by Saturday, 15 December.
FA Youth Cup third-round draw:
1 Sheffield Wednesday v Stoke City
2 Blackburn Rovers v Cheltenham Town or Gillingham
3 Everton v Sunderland or Oldham Athletic
4 Burnley v Oxford United or Barnet
5 Huddersfield Town v Peterborough United
6 Watford v Birmingham City
7 Preston North End v Charlton Athletic or Southend United
8 Leicester City v Fulham
9 Arsenal v Northampton Town or Swindon Town
10 Accrington Stanley or Notts County v Leeds United
11 Wolverhampton Wanderers v Wigan Athletic
12 Hull City v Cardiff City
13 Maidenhead United v Nottingham Forest
or Torquay United
14 Middlesbrough v Sheffield United
15 Bristol City v Salford City or Crewe Alexandra
16 West Bromwich Albion v Lincoln City or South Shields
17 Liverpool v Cray Wanderers or Portsmouth
18 Manchester United v Chelsea
19 West Ham United v Brighton & Hove Albion
20 Southampton v Rotherham United
21 Aston Villa v Swansea City
22 Blackpool v Derby County
23 Ipswich Town v Wingate & Finchley or Andover Town
24 Bolton Wanderers v Newcastle United
25 AFC Bournemouth v Mansfield Town or Chester
26 Stevenage or Exeter City v Bury
27 Cogenhoe United or Coventry City v Crystal Palace
28 Millwall v Tottenham Hotspur
29 Port Vale or Sutton Coldfield Town v Norwich City
30 Clevedon Town or Sutton United v Manchester City
31 Queens Park Rangers v Rochdale or Milton Keynes Dons
32 Yeovil Town or Cambridge United v Reading