The Premier League side are eager to get the winger to stay on similar terms to his current deal.The 35-year-old is out of contract this summer, but The Sun states that he may stick around.
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Manager Marco Silva hopes that he can count on Willian as a regular starter again.
However, there may be a temptation from the ex-Chelsea and Arsenal star to head back to Brazil.
He signed a 12-month deal at the start of last season, helping the club to 13th place.