Chelsea have turned down a bid in excess of £50m for Willian from Barcelona, according to Sky sources.
Talks remain ongoing between the two clubs and representatives of the player, who is currently on international duty with Brazil at the World Cup.
Sky sources understand Barcelona first began efforts to lure Willian to the Nou Camp as long as three months ago.
Sky Sports News reported in May that Manchester United are also interested in signing the versatile winger this summer, with the forward wanting to leave Stamford Bridge if Antonio Conte remained as head coach.
Willian made 55 appearances in all competitions for Chelsea last season, scoring 13 goals.
However, he was left out of the starting line-up for the 1-0 FA Cup final win over United at Wembley, coming on as an injury time substitute.
In total, Willian has scored 44 goals in 236 appearances for Chelsea since joining from Russian side Anzhi Makhachkala in 2013.