The meeting took place in De Laurentiis' Filmauro movie production company building in Rome, and Ancelotti was filmed arrived and departing.
It is being widely reported in Italian media that the meeting was to finalise a three-year contract, for which a basic agreement has been reached, although further talks are expected tomorrow.
This would appear to confirm that current coach Maurizio Sarri, who is still under contract, is set for an imminent Napoli exit after strong links with the coaching positions at Chelsea and Zenit St Petersburg.
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Former banker Sarri has made no public decision yet on his future.
Sky Sport Italia report that Napoli will sack Sarri the moment Ancelotti signs a contract.
There are even rumours that Napoli have a clause allowing them early termination of Sarri's employment for a nominal €500,000 (A$780,000).
Sarri is reportedly unimpressed with an offer he has received from Zenit, while Chelsea are allegedly mulling over their options because Antonio Conte will not resign and his FA Cup victory has owner Roman Abramovich reconsidering firing him.
In that case, the coach - who has won so many plaudits for Napoli's style this season - might take a year off football.