Chelsea's transfer ban means that they are extremely reluctant to sell Willian, according to Sky Sports.
The Brazilian, who is currently playing in the Copa America, is entering the final 12 months of his contract at Stamford Bridge.
However, Chelsea would rather risk losing Willian on a free transfer next summer than not have him available for the coming season.
Eden Hazard completed his move to Real Madrid last week for £88 million (plus add-ons) last week.
Chelsea will reportedly now try to convince Willian to sign a two-year extension at the club.
Barcelona are expected to return for the two-time Premier League winner, however, having tried to sign Willian for the two windows prior to this one.
Meanwhile, Atletico Madrid are looking to plug the whole left by Antoine Griezmann - and have cash to do so.
NOW TRY...
Before the gold rush: remembering Chelsea’s last season before Roman Abramovich arrived
The outsider: how Bernardo Silva could enter the running for this year’s Ballon d’Or
‘He instantly popped into our ratings as one of the best U21 midfielders in Europe. The impressive thing is Slot has made him into more of a no.6' Inside Ryan Gravenberch's transformation at Liverpool
‘I don’t think Liverpool would look at Ollie Watkins, a striker isn’t a pressing issue for them – it’s Arsenal who need one’ Former Reds star explains why his old club don’t need an out-and-out forward this summer
