The Hoops were drawn against the NIFL Premiership champions or S.P. La Fiorita from San Marino.
From a football point of view it is fantastic.
"Celtic are relaxed about it and they seem happy enough to play in Belfast on July 11", Mr McGivern added.
Linfield, who have a close association with the Bhoys' arch-rivals Rangers, have prominent Protestant connections while Celtic's deep association with Irish Catholicism is likely to prompt authorities to look into the possibility of moving the date of the fixture, given its combustible timing.
Blues chairman McGivern said that early talks had taken place with Celtic representatives about the potential tie and said that, for practical reasons, July 12 was not an option.
Should the Blues progress the club will be obliged, under UEFA's ticket allocation rules, to make at least 10% of Windsor Park's 18,000 seats available to the away supporters.
Scheduling: Game would not take place on July 12.
It's good to see that he's not taking his eye off the ball considering that Linfield have to get through the first round first, but it would have been madness not to try and sort this out well in advance.
La Fiorita compete in the Campionato Sammarinese di Calcio which is ranked 53rd of the 54 European leagues graded by UEFA (ahead of Gibraltar).
"I had lunch with Celtic's representatives after the draw and we've had initial discussions about the games".
I'm sure the fans would love nothing more than a game against Celtic.
Brendan Rodgers led Celtic to the domestic treble last season.
"To be honest I would prefer a softer team than Celtic. That is just being realistic", he said.
And having played against the Scottish champions many times during his glittering career, World Cup victor Xavi Hernandez knows how big a club Brendan Rodgers' side are, and loves seeing them play on the biggest stage.
He said: "I'd play in the auto park tomorrow if I needed to".