Antonio Conte rates the forward highly, and revealed last Friday that he tried to sign the then Udinese player when he was Juventus manager.
Chelsea are yet to make a formal offer for Sanchez, but they do have a history of flying under the radar when it comes to signing players.
They bought Willian from Anzhi Makhachkala in 2013 when he was poised to join their London rivals Tottenham.
The news comes on the same day Manchester City pulled out of the race for Sanchez due to their belief the deal had become too expensive.
Manchester United, however, are still interested in the 29-year-old, and Sky Sports News understands they are willing to pay Sanchez more than £350,000 per week if he were to move to Old Trafford.