Ajax lost last season's Europa League final 2-0 to Manchester United and will face a tricky challenge against Lucien Favre's Nice.
Ajax lost last season's Europa League final 2-0 to Manchester United and will face a tricky challenge against Lucien Favre's Nice who finished third in France last term.
Celtic, who face Northern Irish title-holders Linfield in the second qualifying round, would play either League of Ireland champions Dundalk or Norway's Rosenborg if they progress.
The winners of the third-round ties, to be played July 25-26 with the return legs on August 1-2, will advance to the play-off round in search of a place in the lucrative group phase.
Third qualifying round draw:
Steaua Bucharest (ROM) v Viktoria Plzen (CZE)
Nice (FRA) v Ajax (NED)
Dynamo Kiev (UKR) v Young Boys (SUI)
AEK Athens (GRE) v CSKA Moscow (RUS)
Club Brugge (BEL) v Istanbul Basaksehir (TUR)
Slavia Prague (CZE) v BATE Borisov (BLR) or Alashkert FC (ARM)
FK Spartaks Jurmala (LAT) or FC Astana (KAZ) v IFK Mariehamn (FIN) ou Legia Warsaw (POL)
HSK Zrinjski (BIH) or NK Maribor (SLO) v FH Hafnarfjordur (ISL) or Vikingur (FRO)
MSK Zilina (SVK) or FC Copenhagen (DEN) v Malmo (SWE) or FK Vardar (MKD)
Linfield (NIR) or Celtic FC (SCO) v Dundalk (IRL) or Rosenburg (NOR)
Hapoel Beer-Sheva FC (ISR) or Honved (HUN) v Zalgiris (LTU) or Ludogorets (BUL)
Viitorul (ROM) v APOEL (CYP) or Dudelange (LUX)
Hibernians FC (MLT) or Salzburg (AUT) v Rijeka (CRO) or The New Saints (WAL)
Qarabag (AZE) or FC Samtredia (GEO) v Sheriff (MDA) or FK Kukesi (ALB)
Partizan Belgrade (SRB) or Podgorica (MNE) v Olympiakos (GRE)