The Jam Tarts will face either Linfield or FC Zurich for a place in the group stages with the matches taking place on Thursday, August 18 and 25.
As Hearts were drawn second, they are expected to travel to either Belfast or Zurich for the first leg. With the Swiss side 1/14 favourites to advance, many supporters have already booked travel and accommodation.
However, there remains a possibility the venues could be switched with Hearts playing at home first.
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Zurich will be forced to play 80km from their home ground in St Gallen if their home tie remains on August 18 as there is a concert booked for Stadion Letzigrund on the same evening.
The club wrote on Twitter: “Remember folks, please don’t book travel/accommodation until match details - dates, locations, fixture order - are confirmed by UEFA, which we hope will be by tomorrow evening.”