Barcelona and Juventus are understood to be weighing up a pre-contract agreement in January, according to the Mirror.
Willian has been heavily linked with Barcelona before, with the Catalan club reportedly sounding out a move before they signed Malcolm in 2018.
In a new-look Chelsea side layered with youth, Willian finds himself being one of the more experienced heads at Stamford Bridge.
The Brazilian has played a key role in helping guide Lampard's young squad to an impressive third in the Premier League.
Willian has started 11 of the 12 league games for Chelsea so far this season, scoring two goals and providing three assists.
Lampard has been full of praise for the 31-year-old whose contract runs out next summer.
"The word isn’t 'no brainer' because I can’t get involved in the money. That’s up to the club to do," Lampard said.
"But everyone sees how much I’m relying on him, and picking him and in what he is producing, I love him at this football club. So there’s my answer."
Willian is exactly what Lampard needs in terms of the tactical style he's implementing at Chelsea.
"When I looked at him at the start of the season, I saw him being huge for me and the way we want to play" he added.
"The off-the-ball work he's done is an absolutely outstanding example for Callum Hudson-Odoi, Christian Pulisic and other young wingers who think the only part of the game is going past people and crossing or shooting.
"He does the other side brilliantly, with absolute humility, so he's been a joy and one of the experienced players that's really helping the young boys."
Whilst his role appears to be crucial this season, there is reportedly doubt that the situation will be the same after Chelsea's transfer ban is lifted next summer.
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