The Easter Road side play the Greeks in Edinburgh this Thursday, before travelling to Tripoli for the second leg next week.
If Neil Lennon can guide his team through a potentially tricky tie, the Capital club will be unseeded and could face some of Europe’s top clubs.
Among the big guns Hibs could face are La Liga side Sevilla, who finished seventh in the Spanish top tier last season, or AZ Alkmaar of the Netherlands, who came third in the 2017/18 Eredivisie.
Kairat Almaty are another potential opponent although the Kazakh side would have to defeat AZ to progress, while Ujpest of Hungary stand between the Spaniards and the next round.
Norwegian side Molde will battle it out with Laçi of Albania, while Rudar Velenje of Slovenia take on Romania’s Steaua Bucharest.
Austrians Rapid Vienna, who finished third in the league last season, also enter the draw at the QR3 stage.