Conte led Chelsea to the Premier League title in his first season in England in 2016-17 and followed up that achievement with the FA Cup triumph this year, but his relationship with the board became damaged beyond fix, highlighted by his repeated public and private complaints about transfer policy.
The report claimed that Sarri will be announced as the new Chelsea manager within the next 48 hours.
Zola scored 59 league goals for Chelsea across seven seasons between 1996 and 2003.
The Premier League season starts in four weeks' time, leaving clubs much less time than usual to conclude their summer transfer business.
He's set to be appointed imminently after Chelsea confirmed the departure of Antonio Conte.
The Italian had two contrasting campaigns at the helm as he over a team that finished 10th in the Premier League as defending champions and turned them around immediately to reclaim the title in 2016/17. "Great man, Great manager".
Conte also fell out with David Luiz and Willian, and used press conferences last season to accuse the board of not signing his targets.
"We wish Antonio every success in his future career", the statement read.
The Italian's main gripe for the past year was Chelsea's failure to land the signings he really wanted for its Premier League title defence.
Meanwhile, Brazil and Roma goalkeeper Alisson is in talks with the club and could arrive should Thibaut Courtois leave for Real Madrid.
Sarri's future has been up in the air since Napoli hired Carlo Ancelotti as their new coach in May.