Last season's League Cup winners Liverpool have been drawn to face either Renova of Macedonia or Gomel of Belarus in the third qualifying round of the competition they reached the semi-finals of in 2010.
Gomel won the first leg of their second-round tie against Renova 2-0 away, and will be favourites to progress after the second leg on July 26 and meet the Reds in Brendan Rodgers's first competitive game in charge.
Things look significantly tougher for the two Scottish sides entering the competition at this stage, however.
Dundee United will face Dynamo Moscow, who finished fourth in the Russian Premier League last season.
St Johnstone will play Marseille - who won the French league in 2010 and reached the quarter-finals of the champions League last term - if they can overhaul their 2-0 first-leg deficit against Turkish side Eskisehirspor in the second round of qualifying.
Irish club St Patrick's also have a tough draw in prospect if they beat Bosnian club Siroki, as they will face Bundesliga side Hannover.
Thirs qualifying round ties will be played on August 2 and 9, with the winner of each progressing to the play-offs for a place in the Europa League proper.