Linfield have been drawn to face La Fiorita of San Marino in the first round of the competition but if they get through that then the Irish League champions are now scheduled to face the Scottish club on either July 11th or 12th.
The potential date clash raises the real prospect of sectarian trouble in Belfast, the Northern Irish capital.
New Celtic winger Jonny Hayes is looking forward to his club's ties but does not believe the extra spice involved in a potential showdown with Linfield will worry the Hoops too much.
"Financially for Linfield it would be a glamour tie to get Celtic".
The return leg would take place in Glasgow the following week.
The Linfield chairman said that the club was happy to have the first leg of a possible Celtic encounter at home for financial reasons.More news: Tech CEOs to Visit White House; Kushner Speaks
"I had lunch with Celtic's representatives after the draw and we've had initial discussions about the games".
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July 12, also known as the The Twelfth, is an Ulster protestant celebration in Northern Ireland and is signified by marches to celebrate the victory of protestant king William of Orange over catholic king James II at the Battle of the Boyne in 1690.
In his first year in charge Brendan Rodgers led Celtic to the title by a margin of 30 points.
"Before that, we play La Fiorita at home next Wednesday and away the following week and that is the priority now". Being realistic, I don't think there would be any chance of us beating them.
Celtic's Jonny Hayes - a Republic of Ireland worldwide recently signed from Aberdeen - said he has no concerns about the potential clash in Belfast. "I've never really thought about stuff like that off the park".