#1 There are better and more experienced alternatives on the market
As stated earlier, despite its history of acrimonious departures and rapid hiring and firing, the Chelsea managerial job remains one of the most prestigious in the world and is a position which almost all managers would be honored to occupy.
At the moment, Chelsea are spoiled for choice for Sarri's replacement, as there are a number of top-class and proven winners who are currently on the shopping list for new managerial jobs
Recently dismissed Juventus manager has been surrounded with rumours about an offer to head in the other direction as his potential replacement Maurizio Sarri. Meanwhile, former PSG manager Laurent Blanc has also been out of employment since being sacked by the Parisians in 2017.
Elsewhere, Arsene Wenger departed Arsenal in 2018, but never ruled himself out of a return to coaching. In addition, Jose Mourinho could return for a third spell at Stamford Bridge (although the acrimonious nature of his departure could prove a stumbling block).
Looking inwards at the Premier League, Mauricio Pochettino has said he would seriously consider his future at White Hart Lane if the club does not back him financially, while Watford's Javi Gracia is also highly rated after his impressive work at Vicarage Road.
Given the number of highly experienced and proven coaches available to Chelsea as options, it makes no sense for them to hire Frank Lampard at the expense of these proven winners.