34-year-old Ljungberg, who has spent the last 18 months playing in the United States with Seattle Sounders and Chicago Fire, is due to arrive in Glasgow later Sunday.
“Ljungberg is coming in tonight. It is not a trial or anything like that,” said Celtic boss Neil Lennon.
“It’s so that we can have a look at him and he can look at us. We were contacted three or four weeks ago. I don’t think he is over the hill. I think he is 34 but he has always kept himself in good condition.”
“You don’t lose the quality, he might be missing an edge but we will see how he is.”
“He has been a quality player for a long time, he is vastly experienced and again, it’s just an opportunity that might be there for us.”
Celtic need cover for South Korean internationals Cha Du-Ri and Ki Sung-Yueng who scored in Sunday’s 2-0 win over St Johnstone, their last club match before leaving for the Asian Cup in Qatar which starts next month.