Celtic, West Ham, Aberdeen & Inverness learn Euro draws
Celtic will play Qarabag or Rudar Pljevlja in Champions League qualifying if they progress past Stjarnan.
The winner of the second qualifying round tie which Celtic lead 2-0 will be at home against Azerbaijan's Qarabag or Montenegro's Rudar Pljevlja.
West Ham could face Inverness CT or Astra Giurgiu in the Europa League third qualifying round.
And, in the same competition, Aberdeen or HNK Rijeka will take on Alashkert of Armenia or FC Kairat from Kazakhstan.
In the Champions League qualifiers, the winners of Northern Irish champions Crusaders and Skenderbeu will play Ludogorets Razgrad or Milsami Orhei. It is unlikely to be the Belfast side, however, as they lost 4-1 in the first leg in Albania.
Welsh champions The New Saints or Videoton will face BATE Borisov or Dundalk. TNS lost the home leg 1-0, with Irish champions Dundalk losing 2-1 in Belarus.
In Europa League qualifying, Southampton will play manager Ronald Koeman's old side Vitesse as both sides enter the tournament.
Northern Ireland's Linfield, who trail 2-1 to Spartak Trnava, could face Croatia's Lokomotiv Zagreb or Greece's PAOK in the third qualifying round.
And Welsh side Newtown, who are 2-0 down to Copenhagen at the midway stage of the second qualifying round, will take on Czech Republic's Jablonec if they overcome their deficit.
The return leg of Celtic's tie with Stjarnan is on Wednesday, the same night that TNS and Dundalk return to action. Crusaders resume their tie on Tuesday.
Champions League third qualifying round first leg dates are 28 and 29 July, with the return on 4 or 5 August.
Reacting to the draw, Celtic manager Ronny Deila told his club website: "That's the next round. First we have to get finished with this round and play a good game on Wednesday and then we can talk about other things if we do.
"We had a lot of good movement and passing in the game against Stjarnan on Wednesday and I think we should have been more effective. But the result was good - I hoped that we would have won by more, but 2-0 is a good result when we go away."
West Ham and Aberdeen lead their respective ties against Malta's Birkirkara (1-0) and Croatia's Rijeka (3-0). The Hammers are away for Thursday's return leg while the Dons will be at home and look well placed to progress.
Inverness, who are playing in Europe for the first time, trail 1-0 to Romania's Astra, who have an away goal as well as a lead to protect on Thursday.
Europa League third qualifying round first and second qualifying dates are 30 July and 6 August, respectively.