Former champions Chelsea will face Malmo in the last 32 of the Europa League while Arsenal will lock horns again with BATE Borisov.
The two sides met in the Europa League last season, the Gunners hammering the Belarussian side 6-0 at the Emirates.
Five-time champions Sevilla, currently second in La Liga, face a difficult tie against Lazio, beaten finalists in this competition in 1998, who are fifth in Serie A.
The 2004 champions Valencia will have to overcome Celtic if they are to progress to the round of 16 for the first time in three years.
The Scottish side's coach Brendan Rogers says he has been impressed by the Spanish club in Europe this season after they finished third in a Champions League group including Manchester United and Juventus.
"I saw them this season against Manchester United, I thought when they played at Old Trafford they played like a typical Spanish team, technically very good and they have some very good players," he said.
"We have the first game at home and we would like to bring some sort of advantage into the second leg," the Northern Irishman added.
Another Spanish side Villarreal, currently hovering just above the Liga relegation zone, face an Iberian battle when they take on Sporting.
Napoli, demoted to the Europa League after they were knocked out of the Champions League at the group stage, face Zurich.
Portuguese giants Benfica, three times runners-up, tackle Turkish side Galatasaray, UEFA Cup winners in 2000, and Inter Milan, another team who failed to progress to the Champions League knockout stage, will play Rapid Vienna.
The ties will take place on 12-14 and 20-21 February.