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.
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