Liverpool will face Turkish side Trabzonspor in the Europa League play-off round.
Roy Hodgson's side will meet the club based in Trabzon, who have won the Turkish league six times, on August 19 and 26.
The play-off is the final hurdle before qualifying for the group stage, with Friday's draw involving 74 clubs.
Trabzonspor won the Turkish cup last season but have not claimed the league title since 1984.
Aston Villa face Rapid Vienna - Austria's most successful club with 32 championships.
The pair met in the same round last season with Villa crashing out of the competition on away goals.
Manager Martin O'Neill had a premonition that Villa would face Rapid once more and is predicting a challenging tie.
"We had the feeling beforehand that we'd probably find ourselves drawn against Rapid Vienna again," O'Neill told the club's official website.
"As proved to be the case last year, this will be a difficult assignment against difficult opposition.
"But we are looking forward to the game and we will try to do our best to qualify for the group stage.
"This won't be easy because Rapid was as tough a draw as we could have encountered, but we'll be ready to go."
Big-spending Manchester City travel to Romania for the first leg of their play-off after being paired with Timisoara.
The Romanian minnows, established since 2002, finished fifth in their domestic league last season.
City manager boss Roberto Mancini is not expecting an easy ride.
"It will be a difficult game and any team from Romania will provide stiff opposition, particularly on their own ground," he told the club's official website.
"We will look forward to both legs and obviously look to ensure we move to the group stages of the competition."
Welsh outfit TNS also travel for their first leg, heading to Bulgaria to meet CSKA Sofia.
SPL giants Celtic will take on Dutch side Utrecht.
The Hoops' dropped down to European club football's second tier competition after being knocked out of the Champions League qualifiers by Braga on Wednesday night on a 4-2 aggregate.
Neil Lennon's side, who were seeded for the draw in Nyon, will play the first game at home on August 19 before travelling to Holland a week later.
Motherwell will fancy their chances of making the group stages for the first time after being drawn to play Odense, with the first leg in Denmark.
Craig Brown's men have come through two qualifying rounds against Icelandic side Breidablik and Aalesund.
The Norwegian side were beaten 3-0 at Fir Park on Wednesday as the home side cruised through to the play-offs with a a 4-1 aggregate win.
Dundee United will make their first appearance in the Europa League this season when they take on AEK Athens.
The Active Nation Scottish Cup holders were drawn at home in the first leg and will be looking to take a decent lead to Greece for the return game.
Matches will be played on August 19 and 26.
Play-off draw:
Paris Saint-Germain v Maccabi Tel-Aviv
Bayer Leverkusen v Tavriya Simferopol
CSKA Moscow v Anorthosis Famagusta
Hajduk Split v Unirea Urziceni
Feyenoord v Gent
Genk v FC Porto
Debreceni v Litex Lovech
Aris Thessaloniki v Austria Vienna
Galatasaray v Karpaty Lviv
Palermo v Maribor
Club Brugge v Dinamo Minsk
Omonia v Metalist Kharkiv
SC Vaslui v Lille
Napoli v IF Elfsborg
Sporting Lisbon v Brøndby
Grasshopper Zurich v Steaua Bucharest
Liverpool v Trabzonspor
Celtic v FC Utrecht
Borussia Dortmund v FK Qarabag
AIK v Levski Sofia
Sturm Graz v Juventus
Getafe v APOEL
Dundee United v AEK Athens
AZ Alkmaar v FK Aktobe
Dnipro Dnipropetrovsk v Lech Poznan
Rapid Vienna v Aston Villa
CSKA Sofia v The New Saints
Besiktas v HJK Helsinki
Slovan Bratislava v VfB Stuttgart
FC Sibir Novosibirsk v PSV Eindhoven
BATE Borisov v MarÃtimo
Lausanne v Lokomotiv Moskva
Gyori ETO v Dinamo Zagreb
Odense v Motherwell
PAOK v Fenerbahçe
Villarreal v FC Dnepr Mogilev
FC Timisoara v Manchester City
First legs to be played on August 19; second legs on August 26.