With Celtic Park out of commission because of the Commonwealth Games, Ronny Deila is set for a Murrayfield debut as manager with Celtic picked out first in the draw for the second qualifying round, although the final details are yet to be confirmed.
The first leg will take place on July 15-16 with the second leg the following week.
Celtic are set to come up against a former player in striker Kjartan Finnbogason, who joined the Glasgow club from KR in 2004 aged 17 but failed to make a first-team breakthrough under Martin O'Neill and then Gordon Strachan.
The forward moved to Norway in 2007 and scored one goal in eight appearances during a loan spell at Falkirk in 2009 before eventually returning to KR, where he is their top European goalscorer with eight strikes.
The top goalscorer in their title-winning campaign, Gary Martin, was also released by Strachan, at Middlesbrough.
KR currently sit fourth in the league, four points off the top, after taking 16 points from nine games.
Elsehwere in the draw, Northern Irish champions Cliftonville were picked out first against Hungarian side Debreceni.
Welsh side The New Saints are due to open their campaign in Slovakia against Slovan Bratislava and Airtricity League of Ireland champions St Patrick's Athletic will take on Legia Warsaw with the first leg set to be in Poland.
Among the six teams playing in the first qualifying round are Lincoln Red Imps of UEFA newcomers Gibraltar. They face HB Torshavn of the Faroe Islands with the winners then taking on Partizan Belgrade.
Deila was reasonably happy about the draw.
"It could be worse and it could be better," the Norwegian said. "It's an okay draw.
"Reykjavik are a good team and Icelandic football has improved a lot in the last few years.
"We have to treat them with respect but we are favourites and we are going to do everything to win the game."