Club legend Lampard was relieved of his duties in January after a spate of underwhelming results, and former Paris Saint-Germain manager Thomas Tuchel has overseen an immediate turnaround in fortunes since taking the hotseat.
However, the German was supposedly not the first choice of Blues director Marina Granovskaia, with Italian journalist Ciro Venerato claiming that she was keen to welcome Sarri back to the English capital before Roman Abramovich stepped in.
Speaking to RAI Sport, Venerato said: "Chelsea, after having sacked Lampard, wanted Sarri. Marina Granovskaia, in particular, fought for his return.
"Sarri had said 'yes' to Chelsea but Roman Abramovich stopped everything. Sarri's wife and son are pushing for Maurizio's return to Naples."
Sarri spent one season at Stamford Bridge in the 2018-19 campaign, and he has been out of management since ending his stint at Juventus in August 2020, but he is being heavily linked with a return to Napoli amid speculation surrounding Gennaro Gattuso's future.