Sarri, who guided Chelsea to a third-place finish in the Premier League and a Europa League win, will complete a return to Italy after a single season in English football.
Other managers have been linked with the role, but it is understood Lampard is now Chelsea’s top choice to replace the outgoing Italian.
Sky Sports News understands that Derby are braced for an approach from Chelsea for Lampard, but have not yet received one.
Massimiliano Allegri, who had been touted as a potential candidate for the role, announced on Thursday he is to take a year out of football after leaving Juventus.
Lampard enjoyed an impressive debut season in management, leading Derby to the Championship play-off final where they lost 2-1 to Aston Villa.
Chelsea are facing the prospect of a two-window transfer ban but would be appointing two figures with a deep understanding of the club should Lampard return alongside his Derby assistant Jody Morris.
Lampard spent 13 years in west London, winning three Premier League titles, four FA Cups, two League Cups, the Europa League and Champions League, becoming the club’s all-time top goalscorer in the process.
Morris, who started his playing career at Chelsea, impressed as a youth coach at Stamford Bridge before leaving to join Lampard at Derby.
Both have an acute understanding of the club’s youth setup and players who are out on loan, which could be vital given their impending transfer ban.
Chelsea have appealed against their two-window transfer ban imposed by FIFA to the Court of Arbitration for Sport.
If Chelsea appoint Lampard he will be the first English manager to take charge of the club in 23 years.
‘Lampard perfect for Chelsea’
Meanwhile, Jamie Redknapp believes that Derby manager Frank Lampard would be the “perfect person” to replace Sarri as Chelsea manager.
Lampard has been linked to the managerial job at Chelsea following his successful first season at Derby where he lost to Aston Villa in the Championship play-off final in May, and Redknapp feels he would be a good fit at Stamford Bridge.
Speaking at Stamford Bridge ahead of Soccer Aid for Unicef, Redknapp told Sky Sports News: “Frank would be the perfect person. Sarri is still the manager right now so until that changes, if it were to change and if they need a manager next year, they need someone who’s going to come in and stabilise the club.
“They have lost their best player (Eden Hazard) and they have got a transfer embargo for two or three windows, so you need someone that everybody loves and they will give them time.”
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