Liverpool will play Macedonian side Rabotnicki or Mika of Armenia in the third qualifying round of the Europa League.
Their opponents will be confirmed next week after the conclusion of the second qualifying round.
Rabotnicki lead 1-0 after the first leg of their tie against Mika this week.
Scottish Premier League side Hibernian were drawn against either Videoton of Hungary or Slovenia’s Maribor.
Videoton and Maribor drew 1-1 in the first leg of their tie.
The other Scottish side in the draw, Motherwell, will face Norwegian outfit Aalesund if they get past Icelandic league leaders Breidablik.
Craig Brown’s men claimed the upper hand in their tie with a 1-0 win last night.
Liverpool will begin their campaign at home while Hibs will travel to Hungary or Slovenia for the first leg of their tie.
Liverpool’s clash will be the first competitive test for new manager Roy Hodgson, who entered the competition at the same stage with Fulham last season and reached the final.
That remarkable run did much to secure the job as Rafael Benitez’s successor at Anfield position for the 62-year-old this summer.
Liverpool reached the semi-finals of the Europa League last season, having been eliminated from the Champions League, but were beaten by eventual winners Atletico Madrid.
This term they had to settle for a place in the Europa League qualifying rounds after finishing a disappointing seventh in the Barclays Premier League.
There is still some way to go before the group stages of the Europa League begin with the victors in the third qualifying round still having a play-off to negotiate.
It is at that stage the likes of Aston Villa, Manchester City and Dundee United enter the competition.