The Clarets will be on the road in the quarter-finals of the FA Youth Cup if they can get past West Bromwich Albion.
The sixth-round draw has handed the winners of next Tuesday night’s meeting at Curzon Ashton a trip to either Fulham or last season’s beaten finalists Manchester City.
The Clarets beat both West Brom and Fulham on their run to the semi-finals of the competition in 2012.
City, who have lost in four of the last five finals, face Fulham at their Academy Stadium on Thursday, 6 February.
FA Youth Cup sixth-round draw
1 Manchester City or Fulham v Burnley or West Bromwich Albion
2 Chelsea v AFC Bournemouth or Millwall or Wolverhampton Wanderers
3 Manchester United or Leeds United v Wigan Athletic or Birmingham City
4 Blackburn Rovers v Arsenal or Brighton & Hove Albion or Preston North End
Sixth-round ties are scheduled to be played by the end of February.