PSG coach Thomas Tuchel is a target for Chelsea.
Blues boss Maurizio Sarri has emerged as a main contender having impressed Juventus during three years at Napoli between 2015-18.
The Italian still has one year on his contract at Chelsea, although the club have the option to extend it by another 12 months.
While Sarri has insisted he wants to stay at Stamford Bridge, clubs in Italy believe he would welcome a return to Serie A.
The London Evening Standard says possible replacements for Sarri should he leave include former midfielder Frank Lampard, currently in charge of Derby County, and Paris Saint-Germain coach Tuchel.
Departing Juve coach Max Allegri has also been mentioned.