Brendan Rodgers' first competitive game in charge of Liverpool will see him face either FK Renova from Macedonia or FC Gomel in the third qualifying round.
The Reds, who only qualified for the competition by virtue of winning last season's Carling Cup, were seeded in Group Two for clashes that are set to be played on August 2 and 9.
But the three-time winners instead await the winners of a second qualifying round clash, with Gomel taking a 2-0 lead into the second leg on home turf next Thursday.
Gomel, who play at the Central Stadion, are managed by Oleg Kubarev and finished third in the Belarusian Premier League last year, while Renova were fourth in the Macedonian First League.
Rodgers will be looking to make an immediate impact in his first two matches in charge - with the domestic campaign getting under way a little over a week after the Reds play their second leg clash.
Success in the Premier League will be paramount after Liverpool finished eighth last season but Rodgers has already spoken about setting high standards from the off.
The Reds were seeded on Friday alongside Dinamo Moscow, Steaua Bucharest, Bursaspor, the winners of Young Boys v Zimbru Chisinau and Mura 05 v CSKA Sofia.
They could also have faced Ukrainian side FC Arsenal Kyiv or the winners of NK Osijek v Kalmar FF, FC Spartak Trnava v Sligo Rovers and Maccabi Netanya FC v KuPS Kuopio.
Liverpool are currently on a pre-season tour of North America and will play their first pre-season game against Toronto on Saturday.
Dundee United also enter the Europa League at the third qualifying stage and although they avoided Liverpool, they face a tough test against Dynamo Moscow if they are to advance to the play-off round.
The Terrors finished fourth in the Scottish Premier League last season to reach this stage, but were always likely to receive a difficult tie as they were unseeded for the draw.
Dynamo also finished fourth in their domestic league last campaign and will certainly offer a stern challenge for Peter Houston's side.
The first leg will take place at Tannadice on August 2 with the return leg in Russia a week later.
St Johnstone could face French giants Marseille if they can overhaul their 2-0 first-leg deficit against Turkish side Eskisehirspor in the second round of qualifying.
Steve Lomas' Saints lost in Turkey on Thursday night but now have a huge incentive to win the return leg at McDiarmid Park next week to set up a historic and lucrative tie with the nine-time Ligue 1 champions.
The Saints were unlucky to concede two deflected goals against Eskisehirspor but manager Lomas still believes his side are good enough to progress, and a potential match against such illustrious opponents will act as a further spur for his players.
Irish side St Patrick's Athletic could also face a well-known European club in the third qualifying round.
A tie against Hannover is on offer for the winner of the second round match between St Pat's and Siroki Brijeg of Bosnia and Herzegovina, with the scores level at 1-1 following the first leg.
Fellow Irish outfit Sligo Rovers will have to overcome a 3-1 first leg defeat to Slovakian side Spartak Trnava to advance to a tie with Steaua Bucharest.
Northern Ireland side Portadown were drawn opposite last year's beaten finalists Athletic Bilbao.
However they are unlikely to meet the Spanish side due to a 6-0 defeat against Slaven Belupo of Croatia in their second qualifying round first leg last night.
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