Neil Lennon's side are seeded in the second qualifying round draw, with Irish champions Sligo Rovers, Danske Bank Premiership winners Cliftonville and Welsh champions The New Saints among the teams Celtic could face.
The Hoops are among 17 seeds in the draw with all but two of their possible opponents already known - the champions of Andorra, San Marino, Armenia and the Faroe Islands are the only teams playing in the first qualifying round.
Celtic, whose first game will be on July 16 or 17, will have to knock out a total of three teams in order to reach the group stages for a second successive season.
The Europa League second qualifying round fixtures will also be decided on Monday, with Hibernian and St Johnstone among the British sides entering at that stage.
The first qualifying round will be drawn first with Linfield and St Patrick's Athletic among the seeded teams. Glentoran, Crusaders, Drogheda and Welsh sides Airbus FC, Prestatyn and Bala are among the unseeded sides.
St Pat's will be seeded for the second-round draw too with Hibs and St Johnstone unseeded along with Derry City and Linfield. UEFA will split the 80 potential second-round teams into eight groups of 10 on Monday morning to narrow down the potential opponents.
St Johnstone's opening European game on July 18 will be Tommy Wright's first match in charge after he stepped up following the departure of Steve Lomas to Millwall.
Scottish Premier League runners-up Motherwell enter the competition in the third qualifying round.
The Champions League draw takes place at 11am, with the Europa League draw starting an hour later.
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