Celtic will face either Astana of Kazakhstan or Zalgiris Vilnius of Lithuania in the Champions League third qualifying round if they manage to overcome semi-professional side Lincoln Red Imps of Gibraltar.
The Hoops are favourites to reach the next stage despite an embarrassing 1-0 loss to Lincoln in the first leg of their second-round tie.
Manager Brendan Rodgers suffered a humiliating first game in charge when a second-half goal from Ministry of Defence police officer Lee Casciaro condemned the Scottish champions to defeat in Gibraltar.
Should Celtic overturn that deficit in the second leg at Parkhead next Wednesday, they face a long trip to either central Asia, to face Astana, or the Baltics to meet Vilnius.
Meanwhile, Shakhtar Donetsk will start their quest while exiled from their conflict-torn home city for a third season against Young Boys.
Shakhtar have overcome the turmoil of being based in Kiev, and playing in Lviv, to play in the Champions League group stage for the past two seasons.
"Can you imagine we don't have our home, we don't have our fans, we don't have our stadium, we don't have our training camp. We have nothing," Shakhtar CEO Sergei Palkin told The Associated Press.
Shakhtar and Rostov were kept apart by a UEFA rule since 2014 blocking teams from Ukraine and Russia being drawn to play each other.
Rostov, an unheralded regional club in the competition for the first time, were paired with Anderlecht in the third qualifying round. Their reward for advancing could be a playoff against Manchester City, Roma or Porto.
The third-round ties will be played on July 26-27 and Aug. 2-3.
The draw, held in Nyon, Switzerland, was preceded by a moment's silence for the Nice attack on Thursday night.
League Route:
Entering in playoff round (draw Aug. 5): Manchester City, Porto, Villarreal, Borussia Monchengladbach, Roma
Champions Route: