Willian was said to be a target for Barca in pre-season and the Brazil international has caught the attention of the Spanish club once again, according to recent reports.
The 30-year-old's future was discussed following Chelsea's 2-1 Premier League victory over Newcastle United on Saturday, a match in which he scored the winning goal.
When a reporter began to mention the possibility of Willian – whose contract expires in 2020 – only receiving a one-year deal, Sarri cut him short.
"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.
"Maybe he has 12 years of contract, I don't know. I don't know the detail. You are trying to let me speak about something I don't know."
Sarri added: "You know very well that Willian is a very important player for us, as I said yesterday in the news conference.
"In my opinion Willian has to stay with us. A very important player, like Pedro. [Callum] Hudson-Odoi is becoming for us a really important player.
"With Eden [Hazard] as a striker, we need wingers. So we need Pedro. We need Hudson-Odoi. We need Willian of course. For us he's fundamental."
Indeed, Willian himself spoke of the ongoing speculation over his future, telling BT Sport: "My future is Chelsea, I don't know what you're talking about," while fellow goalscorer Pedro added: "Your future is here."
Next up for Chelsea is a trip to Arsenal, where the Blues will hope to put further breathing room between themselves and the fifth-placed Gunners.