The second qualifying round first leg will be the first competitive fixture of the season for Ronny Deila’s men while their opponents are halfway through their domestic season.
Stjarnan have struggled to match last season’s form thus far, garnering only 15 points from 11 league games.
Celtic – who reached the group stages two years ago – failed to qualify last year despite the farrago of the Leiga Warsaw saga, their hopes dashed at the final hurdle by NK Maribor.
Deila said: “We’ve had three good matches and three good weeks with no injuries. You always respect the team but our preparation has been very good. We want to try to get as good a result as possible.
“It’s a little like last year. Icelandic football has gone up, especially the national team. They have a good mentality and produce players but we are prepared and have to go out with 100% tempo and intensity.
“We have no excuses and I’m confident of a good performance. We always want a little more (time to prepare) but we can’t see anything we should have done differently. We’ve had three good matches and three good weeks with no injuries.”
Mikael Lustig missed the Premiership-winning run-in last year after suffering an ankle injury but has played in all three of Celtic’s pre-season friendlies; he hopes to play his part this week.
He said: “Fitness-wise, I would lie if I said I’m in the best shape of my life but it’s getting better. It’s important that I’ve played in three games now and hopefully on Wednesday I’m going to be ready.”
Team-mate Gary Mackay-Steven added: “We have been working on a few things in training and have definitely had good work-outs in the three pre-season games so I’m sure we will be ready for Wednesday.”
Kris Commons will not feature after fracturing his small toe in a domestic accident but new arrival Nadir Ciftci will hope to be involved at some stage after impressing in the 1-0 friendly win over Real Sociedad last Friday.
Another summer signing Dedryck Boyata could also feature after settling in well but Deila could elect to hold fire on former Manchester United defender Saidy Janko. Charlie Mulgrew has also put his injury problems behind him to provide another option.
Dylan McGeouch is back from his loan spell with Hibernian and fellow midfielder Callum McGregor has returned from a fractured ankle, but both also need more time.
It is Stjarnan’s first appearance in the Champions League qualifiers having come to the wider attention of the Scottish public after ending Motherwell’s interest in the Europa League at the qualifying stage last season.
Boss Runar Pall Sigmundsson says his players will have to find another level if they are to be victorious against the Hoops, however, with the side having made a poor start to the defence of their league title, sitting sixth in the table after 11 games.
“Celtic are a big team in Europe, we are a small team,” he said.
“There is a chance of victory but we have to play our best game, every player has to play the game of his life. It will be difficult but there is always a chance.
“They are still preparing for their season so maybe that is an opportunity for us but we have not played so well this season.
“The number one (priority) is to have a great result in the away game. We have a big focus on that, so that we have a chance to have a great game at home.
“It is the first time in the Champions League which is great for us so we are looking forward to playing this game.”