The Clarets have been drawn at home to two-times winners Manchester City or Plymouth Argyle in the fourth round of the FA Youth Cup.
City and Plymouth play next Thursday (14 December) to see who will visit Turf Moor.
The fourth-round ties must be played by Saturday, 20 January.
City won the cup in 1986 and 2008, current Clarets’ captain Ben Mee lifting the trophy nine years ago.
They have also finished runners-up seven times, including each of the last three seasons when they have been beaten by Chelsea in the final.
Burnley, winners in 1968 and semi-finalists in 2012, beat Leeds United 1-0 in the third round.
The Clarets have also been drawn against Manchester City in the FA Cup, with a trip to the Etihad Stadium to come for Sean Dyche's men in round three.