After leaving Brazilian outfit Corinthians, the former returned to the Premier League last summer, signing a one-year deal with Marco Silva's side.
Willian had previously made 339 appearances during a seven-year spell with Chelsea, registering 63 goals and 62 goals.
The former Brazil international then moved on to London rivals Arsenal, but he failed to find his best form at the Emirates Stadium, scoring just one and providing seven assists in 37 games.
However, since returning to the English top flight, Willian has experienced something of a renaissance, contributing to a Fulham side who are currently sat in sixth position.
In his 18 Premier League appearances for the Cottagers, he has scored three goals and registered three assists.
Willian, who currently earns around £40,000 a week, has reportedly enjoyed his time at Craven Cottage and appears to be keen to extend his stay.
While his contract is set to expire in the summer, Silva is hoping to retain his services beyond the end of the season.
As a result, Football Insider are reporting that Fulham are preparing to offer Willian a new deal, which is likely to be an extra one-year extension.
The Cottagers are also believed to be preparing a new contract for left-back Antonee Robinson, who has been attracting interest from a number of clubs.
Newcastle have supposedly made him a top summer transfer target, while there have also been links with Manchester City, AC Milan and Inter Milan.
Robinson currently has a contract until June 2024, but Fulham appear to be keen to tie him down to a new deal as they attempt to ward off potential bidders.
While Willian and Robinson are set to be offered extensions, the futures of Neeskens Kebano, Layvin Kurzawa and Shane Duffy remain uncertain.
As it stands, the trio are all free to leave Craven Cottage when their respective contracts expire at the end of the season.