Speculation over Antonio Conte's future at Chelsea has been rife throughout the season following reports that he has fallen out with the board.
The Blues are reported to be seeking a new man at the helm of the first team, and Sarri is believed to be one of the primary candidates for the role.
According to The Sun, Sarri has been in talks with Chelsea for weeks, despite still being under contract in Naples and with the Premier League side yet to fire Conte.
The report goes on to suggest that the West Londoners are prepared to pay the 59-year-old's £9m release clause, with Zola also making a return to the club as part of his backroom staff.
Zola made upwards of 200 appearances for Chelsea between 1996 and 2003, and has managerial experience in England, having held the reins at West Ham United, Watford and Birmingham City.