According to the Telegraph, they have returned with yet another offer, making Chelsea a player plus cash offer valued at around £50 million, with Barcelona offering fellow Brazilian winger Malcom as part of the deal.
The Spanish giants were hopeful that Malcom would settle in at the club but have now run out of patience with the player.
Brazil global Willian was the subject of strong speculation in pre-season, with Barcelona reportedly having offers for him rejected.
Malcom cost Barca €41million and his slow start has seen a number of transfer and loan links crop up, with Everton originally thought to be front-runners before Marco Silva denied interest.
Bayern Munich are looking to hijack Barcelona's move for PSG midfielder Adrien Rabiot, who was linked with a free transfer to the Nou Camp in the summer.
Nissan cancels lease on Ghosn's Tokyo apartment
It said it took the charges filed against the firm "extremely seriously" and was continuing its investigation into the case. One of his lawyers later conceded that Ghosn could spend a further six months behind bars before his case comes to trial.
Barcelona made a concerted effort to sign Willian in the summer, and sources close to the player have told ESPN FC that he believes they remain interested.
Willian is in his 30's and has not been in the best of form under new manager Maurizio Sarri.
Despite his limited first team opportunities at Liverpool this season, the former Lille star has been able to make an impact on the Reds team chasing honours in both the Premier League and Champions League.
Chelsea have scored the least goals (36) out of the top six and it's Willian's contribution that's most concerning.