"Chelsea, after having sacked Lampard, wanted Sarri," Venerato told RAI Sport. "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."
The claims come 18 months after Sarri left Stamford Bridge to join Juventus – where he only lasted one season before being sacked. Chelsea would eventually turn to fellow agent Thomas Tuchel to succeed Lampard.
Sarri's tumultuous year in west London did end with silverware after he guided the club to Europa League glory.