The Clarets will face either Greek side Olympiakos or Lucerne of Switzerland in the play-off round of the Europa League if they get past Istanbul Basaksehir.
Either Burnley or Basaksehir would be away from home in the first leg following the draw made at UEFA headquarters in Nyon.
The two legs are scheduled to be played on Thursdays 23 and 30 August.
The winners of the play-off ties go into the group stage of the competition.
Burnley go to Turkey to face Basaksehir in the first leg of their third-round qualifying tie on Thursday night, with the return leg at Turf Moor a week later.
Olympiakos are the record 44-time winners of the Greek League but enter the Europa League at the play-off round stage after finishing third in their domestic league last season.
Lucerne, who also finished third in the Swiss top flight last season, are already three games into their domestic campaign – with one win and two defeats.