But if, as expected, they get through, the Hoops could be set to turn back the clock.
Hoping to be lying in wait for Ronny Deila's side in the third qualifying round are St Pat's, the champions from the Irish Republic.
They lost a stoppage-time goal in their first-leg tie against Legia Warsaw in Poland this week to deny them a well-earned 1-0 lead to take into the return match in Dublin.
St Pat's now have the added incentive of a meeting with Celtic, and the chance to atone for allowing to slip through their fingers a golden opportunity to make headlines across Europe the previous occasion the clubs met.
That was in 1998, and the similarities are obvious.
Back then, Celtic had just appointed a new manager, Dr Jo Venglos. And, with the club returning to the European Cup after a decade's absence, the pressure was on to sweep past the Irish underdogs.
However, the first leg at the revamped Celtic Park did not go to plan as over 56,000 fans watched Henrik Larsson, Paul Lambert, Alan Stubbs and Co. stumble to a goalless draw.
It made the trip to Ireland for the return leg a fraught occasion as the spectre of an early exit loomed.
But Harald Brattbakk -whose goal against St Johnstone in the final game of the previous season had set Celtic on their way to the title and preventing 10-in-a-row for Rangers - was the man who calmed the nerves by opening the scoring after 12 minutes.
Larsson added a second mid-way through the second half, and the Hoops - and Dr Jo - avoided a bloody nose.
Former striker Brattbakk recalls the tension which surrounded the ties, and can empathise with how the current crop of players feel as they try to negotiate safe passage through the minefield of the qualifiers and play-offs to reach the Group Stage.
But the man who now earns his living flying planes believes this pressure is simply something everyone who aspires to play for - and manage - the club must accept.
Brattbakk said: "There is always pressure on Celtic to win.
"It was like that when I was there and Dr Jo Venglos was the new manager, and it will be the same now and forever.
"The first game we played with him as manager was against St Pat's, and I don't remember much about it - other than that the result was very disappointing.
"The hype before the match had been intense, because we had finally got the title from Rangers, were back in the European Cup after so long, and we had a new manager.
"Everyone expected an easy win - and that's usually when things don't go as planned.
"That was certainly the case in the game against St Pat's.
"I've been in that situation many times when, if things don't start well, you can lose confidence in yourself.
"So it was obviously very important we won the second leg in Ireland."
Which they did, to give Dr Jo some much-needed breathing space.
Deila is now starting to understand how claustrophobic the air he breathes in the Celtic dug-out can be.
He at least got off to a winning start in Iceland, albeit by the narrowest of margins, and declared himself happy with the performance of his players.
But there is much more needed, and Deila will be looking for improvement in Tuesday's return leg.
Just like Dr Jo, Brattbakk's countryman needs time to find out about his players, while also knowing enough about the opposition to ensure the Hoops do not come a cropper.
Again, the former striker recognises the scenario.
"Ronny Deila, like Dr Jo and any other new manager of the club, needs to find about his players - but he must be winning games at the same time," said Brattbakk.
"He has had four weeks to work with them, which is nothing.
"But a good manager can be expected how to find a decent standard for his team despite so short a period."
Brattbakk watched Deila turn Stromsgodset into unlikely champions of Norway - a title the striker's former club, Rosenborg, had virtually monopolised when he had been banging in the goals for them.
He accepts managing Celtic - and the expectation which comes with the job - is a very different challenge.
But a challenge is something Deila never shirked as a player, and is happy to embrace now he has moved into the dugout.
Brattbakk said: "I remember Ronny was a very good central defender in the Norwegian league.
"He is now a very enthusiastic manager, just as he was as a player.
"I'm not sure what his best qualities are, though he does like to bring through young players and to give them a chance.
"He could afford to do that at Stromsgodset. But at Celtic, you can't sit back and wait for things to happen.
"You have to get results, so I think Ronny might have to rely on the experienced players at the club initially."
It was 21-year-old Callum McGregor who took his chance and scored the all-important goal in Reykjavik, and the attacking midfielder will hope to be in the starting XI again at Murrayfield.
Like everyone else selected by Deila, it will be a step into the unknown at the home of Scottish rugby, where Celtic will have at least one training session after they return from today's friendly in Germany against Dynamo Dresden.
The fact they can't play at Celtic Park for this round or the next as it hosts the Commonwealth Games Opening Ceremony is another hurdle to overcome.
But Brattbakk reckons it really doesn't matter.
He said: "I don't think this is a big problem at these early stages of qualification.
"Celtic should be able to beat a club like KR Reykjavik, even if the home game was moved to Sweden."