Dwayne De Rosario is currently the skipper of Toronto FC in the MLS, and the 32-year-old is hoping a deal can be struck to allow him to make the switch to Parkhead.
Neil Lennon today confirmed the man who has won 55 caps for Canada, scoring 15 goals in the process, is in line to spend time at Lennoxtown to let them see if he might be worth signing.
The Celtic boss still has a central defender and a striker as his priorities when the window opens this weekend.
But he feels he can’t afford not to consider experienced attacking midfielders Ljungberg and De Rosario now that they have become available.
De Rosario has played in Europe, for two years with German club FSV Zwickau when he was a teenager, before moving to the States where he played for, among others, San Jose Earthquakes and Houston Dynamo.
Since he moved back to Canada to play for Toronto FC he has been voted Canadian Player of the Year three times.
This season, De Rosario scored for the MLS-All Star team that lost to Manchester United, and now he wants to test himself on this side of the Atlantic.
He is in the second year of a four-year contract at Toronto, but is unhappy at his wage of £300,000, as it is less than a quarter of what midfield team-mate Julian de Guman receives.
As Lennon prepared to meet with 33-year-old Ljungberg and his agents, the manager explained: “Dwayne might be another one who we may be able to bring in for a week or so to have a look at him.
“He’s a player who has been put to me. I’ve not had time to see much of him. But hopefully today I will get the chance to view some footage of him to see what I think.”
Asked if it will be a case of Ljungberg or De Rosario who gets the chance to bring experience to the squad, Lennon replied: “It could be both. There are opportunities there.
“I’m not saying we are going to sign everyone who comes our way, and I’m not saying this is a done deal.
“But it might just be a little bonus for us along the way without it costing us the earth.”
Ljungberg -- who is a free agent after ending his contract with Chicago Fire -- will have to prove he has fully recovered from the long-term hip problem which required surgery while he was playing in the States.
Lennon said: “Freddie has looked after himself very, very well throughout his career and he has a good mentality towards the game.
“He had a bad time with injuries while he was at West Ham, and I understand that.
“But he has overcome this. He had surgery while he was in America, and for the past 18 months he has been playing on a regular basis.
“Freddie wants to come back and play in Europe. His agents contacted us and we felt there might be an opportunity there to have a look. If he likes what he sees, and we like what we see, there might be a deal worth doing.”
Meantime, after arriving last night to be met by countryman Johan Mjallby at Glasgow Airport, Ljungberg says he is fit and raring to go -- and would love to play against Rangers this Sunday at Ibrox if a deal can be struck.
The former Arsenal man said: “I’ve seen the Old Firm derby on television and I’ve had friends who have been over to the game.
“They said some amazing things about the fixture so, of course, I would love to play in it. I’m available to play for any club on January 1 so we’ll see what happens.
“I’m as fit as I’ve been for a long time since I had surgery on my hip two years ago.”
