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.
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Liverpool have unveiled their new home kit for next season, sticking with the hugely popular retro styling of the current shirt.
The reputation of the Premier League means it is the most popular and one of the most watched leagues in the world.