In the previous campaign, he joined the Cottagers on a free transfer on a one-year deal, after spending the season before with his boyhood club Corinthians.
Willian made a significant impact on Marco Silva’s side, as he scored five goals and provided six assists in his 27 league appearances.
Fulham want to keep Willian at the club, however, the Brazilian winger rejected an initial contract offer with multiple Premier League teams interested in him.
The Craven Cottage outfit offered him another contract offer with improved terms, which the Brazilian has not rejected yet.
It has also been claimed that Nottingham Forest are also aggressively pushing their case to land the free agent this summer.
The Garibaldi have held talks with the 34-year-old winger and are suggested to have put better terms on the table for him.
It remains to be seen which offer Willian finds more tempting to grab and extend his stay for at least another year in the English top flight.