Ljungberg has has spent the last 18 months playing in the USA with Seattle Sounders and Chicago Fire.
“He’s coming in and he’ll have a look at us,” said manager Neil Lennon.
“We think he’s got great calibre. He’s been a world-class player for a long time.”
Ljungberg left West Ham in 2008 after an agreement was reached to terminate his contract.
Meanwhile Celtic struggled to beat St Johnstone at the weekend – and it’s obvious that fans are becoming restless with recent displays.
Injury-time strikes from Korean duo Ki Sung-Yeung and Cha Du-Ri sealed the win and Lennon expressed his gratitude to the club’s fans for their patience.
But it’s clear that patience is wearing thin.
The Hoops travel to Ibrox this Sunday for the Old Firm clash, and Celts fans will be worried that their main rivals could further extend their lead at the top of the league.