Brendan Rodgers' men went unbeaten domestically in a record-breaking 2016-17 season in which they won all three titles available in the coach's first year in charge.
Linfield are heavy favourites against San Marino side SP La Fiorita in the first qualification round, which they'll need to win to book their fixture with Celtic.
CHAMPIONS LEAGUE FIRST QUALIFYING ROUND
|MATCH NO.||SEEDED TEAM||VS||UNSEEDED TEAM||FIRST LEG DATE||SECOND LEG|
|1||The New Saints||vs||Europa FC||JUNE 27/28||JULY 4/5|
|2||Linfield||vs||SP La Fiorita||JUNE 27/28||JULY 4/5|
|3||Vikingur Gota||vs||Trepca 89||JUNE 27/28||JULY 4/5|
|4||Hibernians||vs||FCI Tallinn||JUNE 27/28||JULY 4/5|
|5||FC Santa Coloma||vs||Alashkert FC||JUNE 27/28||JULY 4/5|
The minnows of the Champions League face off against each other later this month and again in the return fixtures at the start of July.
There's a notable all-British tie when Welsh champions The New Saints face Gibraltar's Europa FC.
CHAMPIONS LEAGUE SECOND QUALIFYING ROUND
|SEEDED TEAM||VS||UNSEEDED TEAM||FIRST LEG||SECOND LEG|
|Celtic||vs||Winner of Q1 Match 2||JULY 11/12||JULY 18/19|
|Red Bull Salzburg||vs||Winner of Q1 Match 4||JULY 11/12||JULY 18/19|
|Copenhagen||vs||Zilina||JULY 11/12||JULY 18/19|
|Ludogorets||vs||Zalgiris Vilnius||JULY 11/12||JULY 18/19|
|BATE Borisov||vs||Winner of Q1 Match 5||JULY 11/12||JULY 18/19|
|Legia Warsaw||vs||Mariehamn||JULY 11/12||JULY 18/19|
|APOEL||vs||F91 Dudelange||JULY 11/12||JULY 18/19|
|Maribor||vs||Zrinjski||JULY 11/12||JULY 18/19|
|Qarabag||vs||Samtredia||JULY 11/12||JULY 18/19|
|Malmo||vs||Vardar||JULY 11/12||JULY 18/19|
|Astana||vs||Spartaks Jumala||JULY 11/12||JULY 18/19|
|Partizan||vs||Buducnost Podgorica||JULY 11/12||JULY 18/19|
|Rijeka||vs||Winner of Q1 Match 1||JULY 11/12||JULY 18/19|
|Rosenborg||vs||Dundalk||JULY 11/12||JULY 18/19|
|Sheriff Tiraspol||vs||Kukesi||JULY 11/12||JULY 18/19|
|Hapoel Be'er Shiva||vs||Budapest Honved||JULY 11/12||JULY 18/19|
|FH||vs||Winner of Q1 Match 3||JULY 11/12||JULY 18/19|
Celtic are the biggest team in the draw, with the highest coefficient - how UEFA ranks clubs in continental competition - and the only former European champions at this early stage of the tournament.
Having been drawn against Hibernians FC of Malta or Estonia's FCI Tallinn, Red Bull Salzburg could also cause UEFA a headache.
The governing body's statutes prevent owners from controlling more than one club per season in its competitions, with the higher ranked side in such a situation being given preference.
UEFA were last month quoted as saying: "All criteria, including matters of ownership, will be verified for each club by UEFA only once we have received the competition entry forms and documentation from the national football associations and clubs, following the end of the season in the respective leagues."
Irish champions Dundalk have been drawn against Norwegian side Rosenborg.
WHEN IS THE CHAMPIONS LEAGUE PLAY-OFF DRAW?
Following a third qualification round in which the likes of Nice and Ajax join the fray - that draw is on July 14 - the Champions League play-off round big guns join the elimination round in a draw on August 4.
The Champions League group stage draw will take place on August 24 once all of the qualification and play-off matches are taken care of.