Massimiliano Allegri's future with the champions is under increasing scrutiny after fresh speculation linking him with Arsenal was followed by claims he has already agreed to leave Turin after this season.
Italian newspaper Il Tempo suggested Sarri had held a meeting with Juve to discuss replacing Allegri, but the 58-year-old angrily refuted the report.
"I will speak with the lawyers and see if there are grounds to sue. This being a totally false report, I will see if there are grounds."
Sarri added to reporters: "Now don't go any further, if you do I will get up and leave.
"We will talk about Napoli v Genoa or about Tuesday's game against Real Madrid, or I am going."
Sarri's agent Alessandro Pellegrini was similarly unhappy, insisting the report was an attempt to distract a Napoli side that are flying after winning 7-1 at Bologna last time out and has not tasted defeat since October.
He told Radio CRC: "I cannot comment about something which does not exist.
"It makes no sense to keep talking about something which is meant only to destabilise a team which is starting to be feared."