Celtic will play the first leg away from home which is set to take place on either Tuesday 11th or Wednesday 12th July.
Shamrock Rovers will take on Icelandic outfit Stjarnan with the Hoops on their travels for the opening leg before the return in Tallaght.
Their opponents will become clear in the first week of July after Linfield and La Florita have played each other in the first qualifying round.
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The fire at the 24-story building has led to community anger and protests over the British government's response. British officials have announced a nationwide minute of silence to honor the victims on Monday morning.
It remains to be seen how any issues could be resolved.
The draw for the qualifying rounds of next season's European competition took place at UEFA's headquarters in Nyon on Monday and Brendan Rodgers' treble winners will enter at the second stage. I've got a little bit of experience playing there with Aberdeen where we maybe took our foot off the gas and nearly got punished.
That would mean the Blues travelling to Glasgow on July 11 with the Scottish champions visiting Windsor Park a week later.
Murray : Tennis star in spotlight as Wimbledon looms
World No. 1 Andy Murray has revealed he may only have another "couple of years" playing at the top of the sport. Right now there's a goal towards me doing it. "I'll continue to play so long as my body is fine".
"I'm just happy I've got a chance to finally pull this top on as it could be my first competitive game".
Rodgers, however, got off to a disappointing start twelve months ago when Celtic were beaten 1-0 by part-time Gibraltar club Lincoln Red Imps in July 2016. I keep stressing, we have two very important games before a potential tie with Celtic but it is the best draw would could have hoped for.
I don't think that Celtic should be a club that has to qualify for the Champions League. We're talking player holidays, stag dos and sporting bans, and we even have Dion Fanning taking on the Lottoland Chipping Challenge.
Russia Threatens US: Will Intercept 'Any Flying Object' in Syria Skies
They have very limited capability in Syria by comparison to USA capability, and that's just more talk out of them. The statement said "a number of SDF fighters" were wounded in the regime's attack, but did not specify further.
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