Spanish publication Marca claim the Napoli boss has held talks with Chelsea and the players already believe he is the man on his way to west London.
Conte is set to leave Chelsea in the coming days with Luis Enrique still the favourite to replace him.
But Sarri has hinted he could be leaving Napoli after completing his third year at the club with Carlo Ancelotti set to replace him.
The 59-year-old said: “Everything in life ends and it is better to finish things after writing a beautiful story.
“I don’t know if I will stay, I have to talk about it with my family.
“The situation is complicated. You can’t say you’re ready to go and try again with this squad when you don’t know that everyone will remain here.
“I don’t know if the club will manage to keep the players who have release clauses when offers will come in from big clubs.
“What I do think is that I could not go directly to another Italian team, and that if I had to make a change I would prefer to go abroad.”