The La Liga giants expressed an interest in signing the Brazilian during the summer transfer window, but failed in their pursuit with Chelsea refusing his sale.
According to the Telegraph, they have returned with yet another offer, making Chelsea a player plus cash offer valued at around £50 million, with Barcelona offering fellow Brazilian winger Malcom as part of the deal.
Willian said his future is at Chelsea as he brushed off fresh reports linking him with a move to Barcelona.
But Barcelona are preparing a mammoth bid worth £50m in the hope of luring the attacker away from Stamford Bridge.
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The deal would see Malcom go the other way.
When asked if he would be happy for Willian to leave, Sarri told reporters: "Of course not, because as you know a winger for us is very important. But he's really very important for us so I think it's impossible for us to lose him in January".
"Stop, stop, stop. I don't know anything about the Willian contract, but I don't know what to answer", Sarri said during his post-game news conference. "Normally he wants the ball into his feet, he must improve his movement when he doesn't have the ball and he will have the potential to score more goals".
Chelsea secured a late 2-1 triumph over Newcastle United on the road in the reverse fixture and they can anticipate another tricky test with the Magpies likely to adopt a defensive approach to frustrate them.