European champions Liverpool avoided city rivals Everton in Friday's draw and should play CSKA Sofia in the Champions League third qualifying round.
Twice winners Inter Milan face a tricky trip to Ukraine for the first leg against Shakhtar Donetsk, while four-times European champions Ajax Amsterdam are likely to meet Danish double winners Brondby.
Liverpool were forced to start the defence of their title from the first qualifying round after finishing fifth in the Premier League. They have a 3-1 lead from the away leg of their second qualifying round tie against Lithuania's FBK Kaunas.
Bulgarian champions CSKA Sofia also look likely to win through after a 2-0 first leg victory in Tirana.
"The main thing was avoiding Everton so that's fine," said Liverpool's chief executive Rick Parry. "Inevitably we were relieved not to play someone at the top of the list but it's a long way to travel.
"We treat everyone with respect but not fear."
Twice European champions Manchester United were drawn against the winners of the tie between Debrecen and Hajduk Split of Croatia with the Hungarian champions in the driving seat after a 3-0 win in the first leg.
"Last season was the first time in our history that we won the league title so this is a great reward," Debrecen spokesman Marton Esterhazy said.
"It's easily our biggest game and a great chance for the players to show how strong they are. But first we have a big match in Split on Wednesday."
Everton take on Spanish side Villarreal as both clubs embark on their maiden Champions League campaigns, while Italy's Udinese take on Portugal's Sporting Lisbon, losing finalists in last year's UEFA Cup.
"It's just lovely to be here, part of you thinks it's a miracle," said Everton chairman Bill Kenwright. "We have to accept it as the opportunity that it is to get through to the group stages."
Germany's Werder Bremen meet Swiss team Basel, and French club Monaco, Champions League runners-up in 2004, take on Spain's Real Betis.
Scottish champions Rangers meet Anorthosis Famagusta of Cyprus or Turkey's Trabzonspor.
Their great rivals Celtic are unlikely to make it through to face Partizan Belgrade of Serbia & Montenegro or Sherif Tiraspol of Moldova after losing 5-0 in the first leg of their second round qualifier against Artmedia Petrzalka.
Steaua Bucharest, the 1986 European champions, will play Norway's Rosenborg if they overcome Ireland's Shelbourne.
The two-legged ties take place on August 9 and 10, and August 23 and 24 with the winners going through to the group stage of the competition.