Reports suggest the Blues are considering making a move for the 26-year-old midfielder.
Lulic has also been strongly linked with a move to Bundesliga giants Bayern Munich.
The midfielder has refused to sign a new deal with Lazio, according to The Mirror.
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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.