The Brazil international made his 300th appearance for the Blues in midweek, netting the winning goal in the Champions League victory against Lille.
However, the playmaker has less than a year remaining on his existing deal, putting the 31-year-old in a position where he can hold discussions with foreign clubs in January.
According to The Express, Chelsea are prepared to react by offering Willian fresh terms, a move which is expected to be welcomed by the winger.
The report claims that Willian is keen to extend his stay at the Premier League giants with his family settled in England's capital.
While showing a desire to use several of the club's academy players, manager Frank Lampard is also said to want Willian to stay at Stamford Bridge.body check tags ::