Hibs face the prospect of playing Aston Villa in the Europa Conference League play-off if they can defeat Swiss side Luzern, while Hearts have a potential tie against Hajduk Split or PAOK.
UEFA conducted the draw for the play-offs on Monday and Lee Johnson and his Hibs players now know the route to the group stage, but would have to pull off a huge upset against the English Premier League side.
The match would also see Scotland international and Villa midfielder return to play against one of his former clubs.
Hibs lost the first leg of their second qualifying round game 2-1 to Andorran minnows Inter Club d’Escaldes but were 6-1 winners in the second leg to turn the tie around and progress.
They now welcome Luzern to Easter Road on Thursday before playing the return match in Switzerland seven days later.
The play-off tie would take place on August 24 and 31, with Hibs at home in the first game.
Hearts face Rosenborg in their third qualifying round tie, beginning with the away tie in Norway on Thursday. Their reward for progressing would be a play-off against Hajduk Split or PAOK.
The first leg of that tie would be at Tynecastle, with the return game in Croatia or Greece a week later.