Here are five facts about him...
1) Lulic, 26, is a Bosnian international teammate of Manchester City star Edin Dzeko, with 18 caps to his name.
2) Due to the war in his country in the early 90s, he emigrated to Switzerland with his family, where he began his career, rising up through the Swiss football ranks to play for both Grasshoppers and Young Boys.
3) His performances impressed Lazio enough to spend £2.5 million on signing him in summer of 2011, where he has made 49 appearances to date.
4) This season he has played seven times in Serie A, which include five starts at left-back, and two on the left-wing.
5) His nickname in Italy is 'The Train' for the way he consistently gets up and down the left flank, with seemingly never-ending energy, and he is also renowned for his pace and dribbling ability.
Watch him in action below...
Analysis: Do Chelsea need him? Most would argue that Ryan Bertrand will be Ashley Cole's replacement, should the defender choose to leave the club. Cole, 31, is unhappy at only being offered a one-year contract extension, and will be free to negotiate with clubs from January. Even with Bertrand, this would leave Chelsea seeking a cover in the position, and Lulic at 26 is the right age and experience.
His versatility is another plus, like Bertrand he is able to play in midfield, which would increase his chances of game time. He has a contract until 2016, but the Mirror claim he has turned down a further extension. Lazio may be tempted to cash in on a player they paid just £2.5 million Euros for if an offer comes in which enables them to make a tidy profit.
Would Lulic be a good buy? Should they keep Cole?
image: © Ben Sutherland