Fulham want to restart contract negotiations with Willian in a bid to keep him at Craven Cottage.
The 34-year-old has become a free agent this summer and last month turned down the offer of a new deal.
Willian feels he proved last season that he can still perform in the Premier League and believes he deserves improved terms.
He scored five goals and registered six assists in 27 games for Fulham in 2022/23, playing a key role as Fulham secured a top-half finish in the Premier League under Marco Silva.
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Willian is keen to remain in the Premier League if he leaves Fulham.
He particularly enjoys living in London, having spent seven good years at Chelsea and also played for Arsenal, which gives Fulham hope they will ultimately find an agreement to keep him at the club.
Fulham manager Silva is particularly keen to tie down Willian to a new deal having lost loanee Manor Solomon to Tottenham.
Meanwhile, Tosin Adarabioyo, Antonee Robinson and Kenny Tete all face uncertain futures at Fulham.
But star midfielder Joao Palhinha, who is attracting serious interest from West Ham, has been valued at £90million, which has effectively ended any chance of him leaving.