League of Ireland Premier Division side Bohemians and Greek Super League outfit PAOK meet in the 3QR and the winners of that tie will play the Capital club or the Croatians.
Bohs saw off Stjarnan from Iceland 4-1 on aggregate in the first qualifying round before a comprehensive 4-0 aggregate victory over Luxembourg’s F91 Dudelange in the 2QR.
The Northsiders have won 16 of their 71 European matches including a famous victory over Aberdeen in the 2000/01 UEFA Cup.
PAOK, meanwhile, have reached the knock-out rounds of the UEFA Cup / Europa League on 11 occasions.
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They have won 72 of their 200 matches in continental competition, drawing 58 and losing 70.
The only Scottish club the three-time Greek champions have so far faced in Europe is Rangers, who beat them 2-0 on aggregate during the 1998/99 UEFA Cup.
Hibs have twice faced Greek opposition in Europe, eliminating Asteras Tripolis from the Europa League qualifying rounds in 2018 and losing 4-3 on aggregate to AEK Athens in the 2001/02 UEFA Cup despite a famous 3-2 win in Edinburgh.
The Easter Road side face Rijeka at home on Thursday, August 5 before travelling to Croatia for the return leg a week later.
Should they triumph, Hibs will contest the play-off round matches on August 19 and 25 with the first leg away from home.