The 34-year-old had turned down the chance to stay at Fulham after rejecting an initial offer.
After signing a one-year deal last summer, Willian was keen on improved terms following an impressive season.
Fulham boss Marco Silva was desperate for the Brazilian to stay at Craven Cottage and talkSPORT understands that the west London outfit have now offered him improved terms.
And Willian is ready to put pen to paper and remain at Fulham after his contract had initially expired at the end of June.
The veteran forward played 27 Premier League games last season as the Cottagers had a fine return to the top-flight.
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He scored five and assisted five, including a goal-of-the-season contender against Nottingham Forest.
One of Willian's strikes also helped down his previous employers Chelsea, where he spent seven years of his career.
He made 339 appearances for the Blues, winning the Premier League, Europa League and FA Cup before leaving on a free transfer in 2020.
Arsenal snapped the Brazil international up but not for long after a disappointing campaign that saw him score just once in 37 appearances.
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Willian agreed to mutually terminate his contract at the Emirates before returning to his homeland to join Corinthians.
But that stint did not go to plan, either, netting one goal in 45 appearances before a shock transfer back to the Premier League with Fulham.
Despite age looking like it was starting to catch up with the winger, Willian has proved his doubters wrong by becoming a key player at Craven Cottage.
Willian is well-settled in London, where his family reside and has grown up since making the move to the capital in 2013.
Fulham finished 10th last season in a fine campaign for Silva, who helped the club return to the top tier last year in the Championship.
And the Portuguese coach is ready to splash the cash to make sure they stay there.
Benfica star Morato is on his wish list as a long-term replacement for Tim Ream, who will turn 36 in October.
Leeds star Rodrigo and Southampton midfielder James Ward-Prowse are also on their wish list as they look to pinch players off the relegated teams.