Barcelona have offered Chelsea just over £55m for Willian.
Manchester United have also shown an interest in the Brazilian, who has been at Stamford Bridge since 2013.
Barca have had a previous approach for Willian, 29, rejected by Chelsea but have returned with an improved offer.
Willian, who featured for Brazil in the recent World Cup, has made 169 Premier League appearances for the Blues, scoring 25 goals.
He backed out of a move to Tottenham in order to join Chelsea from Russian club Anzhi Makhachkala for £32m.
His five years at the Bridge included a spell under United’s former Chelsea boss Jose Mourinho, who would like to be reunited with him at Old Trafford.
Meanwhile, Chelsea appear to be edging closer to deal to sign Italy defender Daniele Rugani from Juventus.
This post was last modified on 21/07/2018