Bohemians could face Scottish Premiership side Hibernian, while Dundalk are in line to take on Belgian record champions Anderlecht should the SSE Airtricity League sides reach the UEFA Europa Conference League play-off round.
Shamrock Rovers will face the losers of the Europa League third qualifying round tie between Cyprus' Omonoia and Estonia's Flora Tallinn should the reigning League of Ireland champions progress past Albanian side Teuta in the Champions' path of the qualifiers.
Bohs face Greek Superleague side PAOK in their third-round first leg at the Aviva Stadium on Tuesday. If they advance to the next round, Keith Long's side will face the winners of Hibs' tie with Croatia's HNK Rijeka.
Dundalk visit Netherlands' Vitesse Arnhem for their third-round first leg on Thursday and, if they knock out their Eredivisie opponents over two legs, it will be Anderlecht or Albania's Laç next for Vinny Perth's team for a place in the group stages.
Elsewhere, Tottenham will take on Portuguese side Pacos de Ferreira or Larne in their European opener.
Spurs will be away for the Europa Conference League play-off first leg on 19 August.
Aberdeen will take on Cypriots Limassol or Qarabag of Azerbaijan if they beat Breidablik.
