The controversial Italian looks set to leave the San Siro in the coming weeks after a turbulent spell at the club.
This has alerted the Blues, who are believed to be keen to land a new front-man to keep their title challenge on track.
Jose Mourinho and Balotelli famously have a frosty relationship after their spell together at Inter Milan, but it is thought that the Portuguese boss may be willing to put that in the past with the need for goals in his team high.
AC are still paying instalments to Manchester City for the 23-year-old, which could open the door for a quick sale, especially with the player himself appearing to have no future at the club.
Balotelli himself is believed to be keen on a return to England, where he enjoyed a title-winning stint with the Sky Blues prior to leaving them last year.
Meanwhile, Juan Mata could leave Chelsea before the January transfer window closes.
Atletico Madrid are thought to be leading the race for the Spaniard, who has grown frustrated at his lack of playing time at Stamford Bridge.