Lampard - the club's all-time leading goalscorer - would become Roman Abramovich's third appointment in three years, following in the footsteps of Sarri and new Inter boss Antonio Conte.
Speaking on Monday, Rams owner Mel Morris affirmed: "We've made it clear to everyone, but most importantly to Frank, that we want to retain him for the long term". The Italian coach also set a new record after going unbeaten in his first 12 Premier League games, the longest unbeaten start by any manager in the competition.
However, it is claimed in the same story that Derby County still hope to keep hold of Lampard after he guided them to the Championship play-off final last season.
If Chelsea want to hire him, then they have to make an offer in pursuit of that.
Expect to pay $6,000 if you want to see Pakistan vs India
They already paid Rs.180 crores to broadcasters and advertisers of the 2019 ICC World Cup because of the three cancelled matches due to rain.
In the meantime, we will continue to put our best foot forward to continue with our plans for the coming season. Both clubs have been contacted for comment by Press Association Sport.
The Blues and Juventus have agreed a compensation package, understood to be in excess of £5million, for Sarri, 60, who signed a three-year deal with Chelsea when appointed last summer.
"I think it would be a major surprise if he doesn't get the job".
"It would be brilliant for him".
Following the departure of Massimiliano Allegri from Juventus last month, the Chelsea boss has been heavily linked with Napoli's northern rivals, with Sarri himself having started his desire to return to Italy in a recent interview with GQ.