Lustig is available on a free transfer as his contract with Norwegian side Rosenborg is due to expire.
The 24-year-old has also been linked with a move to Espanyol and Fulham.
Lustig has confirmed he would be interested in a move to Scottish giants Celtic.
“He’s a right-back who plays in Norway but he is Swedish. He is a player we have been tracking for a while,” said Celtic boss Mikael Lustig.