The Blues have been linked with the Bosnian ace for some time, with the 28-year-old having been in impressive form since his 2011 move to the Stadio Olimpico from Young Boys.
Lulic enjoyed an excellent 2012/13 campaign – in which he netted the Coppa Italia final-winning goal against bitter rivals Roma – but he has had a less successful season this time around.
This has led to talk that the Serie A side are ready to cut him loose, alerting Chelsea.
The experienced star is comfortable in either a left midfield of left-back role, and is valued at around £9m.
The Blues are known to be keen to draft in a replacement for Ashley Cole, and could be attracted to Lulic’s ability to support the attack from a deep position.
As well as the Premier League leaders, Inter Milan, Juventus and a number of German clubs are also watching the talented star.
Lulic’s value may well increase this summer, as he look likely to be involved in his nation’s World Cup campaign.