Chelsea are reportedly yet to enter discussions with Derby County boss Frank Lampard, despite holding an interest in the club legend.
That has allegedly resulted in the Blues drawing up a six-man shortlist, which includes Lampard after his impressive first campaign in the dugout.
However, according to The Sun, the West Londoners will only begin talks with Lampard if Sarri completes a switch to Turin.
A number of Chelsea officials are said to be keen for Sarri to stay in West London, although there have been claims that the Italian is craving a return to his homeland.
Meanwhile, the Premier League side appear set to serve the first half of their two-window transfer ban this summer.