The 31-year-old’s current contract will expire when the Blues’ Champions League campaign concludes this month.
Frank Lampard’s injury-hit side face an uphill battle to overturn a 3-0 first leg deficit to Bayern Munich in their round-of-16 meeting this weekend.
The Guardian claim Chelsea have been unable to persuade Willian to sign a new two-year deal, with the winger wanting fresh terms until 2023.
And after his latest contract rejection, Willian’s departure for nothing is all the more likely.
The Brazilian missed Chelsea’s FA Cup final defeat to Arsenal with an unspecified injury and could have played his last game for the club.
Lampard remained uncertain over Willian’s future after Chelsea’s Wembley loss.
He said: “It is his decision, I haven’t got that answer. I know the situation at the club’s end.
“I have a great relationship with Willian, but I don’t actually know what the decision is.
“If that happens over the next whatever days, as he said, then that would be good for me in either way.
“Of course, I am very happy with Willian. He has been brilliant for me this season with his input and work ethic, within the squad.
“But it is his choice and I respect his choice. He has been a great servant for Chelsea if he decides to move on, and if he does decide to move on then Chelsea will move on and we have to look forwards ourselves.”
Willian has won two Premier League titles, one League Cup and the Europa League since joining Chelsea for £30million from Anzhi Makhachkala in 2013.
Last week, Willian’s agent, Kia Joorabchain, confirmed to talkSPORT the player has two offers on the table from Premier League clubs.
“I don’t think he’s done a U-turn or any kind of turn,” he said when asked about his client’s future. “He’s always been very much the same mode.
“We had two very big offers – one from MLS which required him to move on July 1 – but he’s always been in the same mode, saying, ‘I want to finish the season at Chelsea and the day after the season has finished I will make my decision’.
“He has two concrete offers from Premier League clubs on the table, he has an MLS offer on the table which is very big, and he’s got two other offers in Europe
“So Willian is in a very good position and he is going to make his decision after the last game of the season.”