Celtic assistant manager John Collins describes Kris Commons as a "small doubt" for the Champions League qualifier against Stjarnan.
The midfield fractured his small toe in an accident at home and has been restricted to training in the gym for a week while it heals.
"Hopefully, in the next couple of days Kris should be back training on the grass," said Collins.
"I'm led to believe something fell on him - a wardrobe door or something."
Celtic are at home to the Icelandic champions on 14 July, with the return leg a week later.
And Commons, 31, brings a wealth of experience, having played in 37 European ties since moving to Glasgow from Derby in January 2011.
"It's disappointing he's missed a week of training, but he still has a good fitness level," added Collins. "We'll see if he's ready for the matches."
Collins refused to discuss Celtic's rejected £900,000 bid for Dundee United striker Nadir Ciftci.
However, he said that the club are looking to improve in every area of the pitch, with defender Dedryck Boyata already recruited from Manchester City.
"I don't want to talk about players at other clubs, that would be disrespectful, but everybody knows we're looking for new players and we're looking at a lot of players," he explained.
"We're looking to strengthen every part of the team but at the top of the pitch we'd like another player in there.
"We've got good strikers but we've got a lot of games to play.
"There's a possibility [of signings before the qualifiers] but we've got a terrific squad anyway."