Antonio Conte is thought to be a huge fan of the player who has impressed in Serie A this season.
Talks between the two clubs are reportedly underway but only believed to be at a very early stage with the Blues facing competition from Juventus.
Since leaving Liverpool in the search of regular first-team football, the Spanish midfielder has flourished for AC Milan, with six goals and seven assists to his name this season.
Suso is a tricky winger who is likely to fit into Conte’s system in a similar way Pedro does.
The midfielder was reportedly linked with a move away from the Italian outfit last summer but boss Vincenzo Montella was keen to keep hold of him.
With a call-up to the Spanish national team thought to be on the horizon, interest in the player is likely to be high.