Besiktas are to play Group H leaders Lokomotiv Moscow -- who they currently trail by two points -- in the Russian capital while fellow Istanbul side Fenerbahce host Ajax in a Group A fixture that pits fourth against third.
"This is the one trophy that is missing from my collection," Besiktas' German striker Mario Gomez told UEFA.com.
"It is a dream and a target for all of us. I've won the Champions League, been a domestic champion and cup winner, so basically I have won everything at club level -- except the Europa League."
Besiktas will be hamstrung by the absence of striker Olcay Sahan through suspension, as well as missing Veli Kavlak and Tolgay Arslan through injury.
Brazilian left-back Ramon Motta is not on the club's list of players for the competition, so also misses the 7 p.m. CET (1700GMT) kick-off.
Fenerbahce will be looking to their string of high-profile summer signings to drag them off the bottom of their group with their first win.
"We will play against an opponent with a tradition and football culture," manager Vitor Pereira said at a pre-match news conference. "They like to possess the ball and play offensively. Both teams want to win. I believe it will be a good quality match."
Fenerbahce midfielder Mehmet Topal added: "We want to turn a fresh page by leaving all negative things aside. We want to get three points by doing our best."
To achieve that, the club may have to do without Nani, who sustained an injury at the weekend. Volkan Sen, Bruno Alves and Raul Meireles are also out with injuries for the 9.05 p.m. CET (1905 GMT) game at the Sukru Saracoglu stadium.
Thursday sees 24 Europa group matches. The fixtures are as follows:
Qabala (Azerbaijan) - Borussia Dortmund (Germany)
Lazio (Italy) - Rosenborg (Norway)
Dnipro (Ukraine) - Saint-Etienne (France)
Lokomotiv Moscow (Russia) - Besiktas (Turkey)
Sporting Lisbon (Portugal) - Skenderbeu (Albania)
Basel (Switzerland) - Belenenses (Portugal)
Fiorentina (Italy) - Lech (Poland)
Monaco (France) - Qarabag (Azerbaijan)
Anderlecht (Belgium) - Tottenham Hotspur (England)
Schalke 04 (Germany) - Sparta Prague (Czech Republic)
APOEL (Greek Cypriot Adm.) - Asteras (Greece)
AZ Alkmaar (Netherlands) - Augsburg (Germany)
Partizan (Serbia) - Athletic Bilbao (Spain)
Legia (Poland) - Club Brugge (Belgium)
Midtjylland (Denmark) - Napoli (Italy)
Villarreal (Spain) - Dinamo Minsk (Belarus)
Rapid Wien (Austria) - Viktoria Plzen (Czech Republic)
Braga (Portugal) - Olympique Marseille (France)
Slovan Liberec (Czech Republic) - Groningen (Netherlands)
Molde (Norway) - Celtic (Scotland)
Fenerbahce (Turkey) - Ajax (Netherlands)
Liverpool (England) - Rubin Kazan (Russia)
Bordeaux (France) - Sion (Switzerland)
PAOK (Greece) - Krasnodar (Russia)
