Former Champions League finalists Monaco face a tricky third qualifying round tie against Turkey's Fenerbahce after the draw was made in Nyon on Friday.
Monaco, who were beaten 3-0 by Jose Mourinho's Porto in the 2004 final, finished third in France's Ligue 1 last season while Fenerbahce came second to Besiktas in the Turkish top flight.
Ex-Manchester United strikers Radamel Falcao and Robin van Persie could line up against each other after the former returned to Monaco in the close season following unsuccessful loan spells at Old Trafford and then Chelsea.
Four-time European champions Ajax were drawn against PAOK of Greece, with 2009 UEFA Cup winners Shakhtar Donetsk taking on Switzerland's Young Boys and Anderlecht playing surprise Russian Premier League runners-up Rostov.
Celtic must recover from a shock 1-0 defeat to Gibraltar part-timers Lincoln Red Imps in the first leg of their second round qualifier to keep their Champions League hopes alive.
Brendan Rodgers' side will face the winner between Zalgiris Vilnius and Astana should Celtic overturn their one-goal deficit in next week's return fixture in Glasgow.
Third round ties will be played July 26-27 and August 2-3 with the winners advancing to the play-off round, the final qualifying phase before the group stage.
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