The three-time champions, who dropped out of the UEFA Champions League after finishing third in Group B, will host Mustafa Resit Akcay's men in Turin before making the trip to the Huseyin Avni Aker Stadium for the second leg.
Antonio Conte’s Serie A leaders face the prospect of all-Italian clash with Fiorentina in the last 16 should the Florence side overcome Esbjerg of Denmark.
Juve's fellow Serie A rivals Napoli - winners of the competition in 1989 - take on Michael Laudrup's Swansea City, the Welsh side competing in the latter stages of a European competition for the first team in their history.
Rafael Benitez won the competition with Chelsea last season, but his team could face a tough task if they progress to the last 16, with Porto – who take on Bundesliga side Eintracht Frankfurt – their prospective opponents.
Meanwhile, two-time winners Tottenham, now managerless after parting company with Andre Villas-Boas on Monday, will meet Ukrainian outfit Dnipro – managed by former Tottenham boss Juande Ramos - as they aim to improve on their run to the quarter-finals last season.
A clash with Tottenham will be Benfica’s reward should they beat Greek side PAOK, while fierce rivals Real Betis and Sevilla will do battle for a place in the last eight if they negotiate their respective ties against Rubin Kazan and Maribor.
Last season’s semi-finalists Basel face Israel’s Maccabi Tel-Aviv, and they will take on either Ajax or Red Bull Salzburg – who finished the group stage with a 100 per cent record - if they qualify for the last 16.
Valencia continue their quest to repeat their 2004 triumph against Dynamo Kiev, 2009 winners Shakhtar Donetsk meet Viktoria Plzen and Lyon take on Chornomorets Odesa.
UEFA Europa League round of 32 draw:
Dnipro v Tottenham
Real Betis v Rubin Kazan
Swansea City v Napoli
Juventus v Trabzonspor
Maribor v Sevilla
Viktoria Plzen v Shakhtar Donetsk
Chornomorets Odesa v Lyon
Lazio v Ludogorets
Esbjerg v Fiorentina
Ajax v Salzburg
Maccabi Tel-Aviv v Basel
Porto v Eintracht Frankfurt
Anzhi Makhachkala v Genk
Dynamo Kiev v Valencia
PAOK v Benfica
Slovan Liberec v AZ
