Linfield’s first meeting with Celtic could be held on 11 July in Belfast if the Blues reach the second qualifying round of the Champions League.
The clubs discussed arrangements for a potential match, should Linfield first defeat La Fiorita of San Marino, after Monday’s draw in Switzerland.
The schedule date for the match is problematic as it coincides with the ‘Twelfth’ marches in Northern Ireland.
Linfield have proposed an early kick-off, which Celtic are amenable to.
Blues chairman Roy McGivern told BBC Sport the club has provisionally suggested a 17:00 or 17:30 kick-off on Tuesday, 11 July, subject to consultation with the Police Service of Northern Ireland.
McGivern said playing the home leg first is still “the preferred choice” of the Irish Premiership champions.
David Healy’s side will host La Fiorita at Windsor Park on 27/28 June, with the return leg on 4/5 July.
If the Blues progress, they will play the 1967 European Cup winners for the first time.
Celtic defeated Irish League opposition in Belfast four years ago with a 3-0 win over Cliftonville in a Champions League qualifier.
Meanwhile, in the Europa League qualifiers Crusaders take on Latvians FK Liepaja and Ballymena meet Odd BK of Norway.
Coleraine’s opponents FC Haugesund are also from Norway while Derry City go up against FC Midtjylland of Denmark.
The Europa League first qualifying round games will be played on 29 June and 6 July.
|Champions League first qualifying round|
|Linfield||v||SP La Fiorita|
|Europa League first qualifying round|
|Odd BK||v||Ballymena Utd|
|FC Midtjylland||v||Derry City|
|Levadia Tallinn||v||Cork City|