Sky Sports News reported the Blues rebuffed the offers even though Willian, 30, is entering the final year of his contract, as they are eager to keep hold of him.
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Chelsea will be keen to retain as much talent as possible this summer after FIFA suspended the club from registering new players for the next two transfer windows.
Barcelona were linked with Willian in 2018. Jason Burt of the Telegraph wrote in January of this year that the Blaugrana were interested in a deal that could see Malcom move in the other direction.
Willian said at the end of the 2018-19 campaign that he would be saddened to see his Belgian team-mate leave Stamford Bridge, via Soccer AM:
Hazard's exit represents a big loss for Chelsea in a summer where they're not permitted to sign a replacement. The club also recently released manager Maurizio Sarri so that he could join Juventus, per BBC Sport.
Willian took to Twitter to express his disappointment after Hazard's departure was confirmed:
Eden, my brother, it was an honor to play with you in those 6 years! I hope you have success in your new challenge! 💪🏿 Eden, meu irmão, foi uma honra jogar ao seu lado nesses 6 anos! Espero que você tenha muito sucesso em seu novo desafio! 💪🏿 #cfc #hazard #irmao https://t.co/03ykZsaVFk
Sarri fielded Willian 56 times in all competitions last season, and the Brazilian will be looked upon as a senior figure for west Londoners in the post-Hazard era.
Despite the fact that it's possible he could leave the club for free next summer when his contract expires, it appears even the preying eyes of Barca and Atleti won't budge Chelsea from their stance.
Willian's reputation has gone through good and bad patches since he joined Chelsea from Anzhi Makhachkala in 2013, but Statman Dave illustrated his importance to their UEFA Europa League title-winning campaign:
It appears Atletico are making manoeuvres to improve their attack in particular after Record (h/t David G. Medina of Marca) reported they could be on the verge of signing Benfica wonderkid Joao Felix.
Chelsea have the financial backing to be able to resist offers despite their transfer suspension, but Barcelona and Atletico also have the kind of resources that could grasp their attention.