Juventus is trying to negotiate a deal without the need for compensation, but Chelsea is holding out for the majority of the final year of Sarri's contract, worth around £5.3 million, Sky Sports News reported.
Any agreement for the 60-year-old to head back to Italy will then prompt an official approach from Chelsea to Derby for permission to speak to Lampard about becoming Roman Abramovich's 12th manager in 16 years.
Derby has not yet received any approach for Lampard, Sky Sports News understands.
Lampard said he would discuss his future with Derby after the club failed to win promotion to the Premier League following its playoff final defeat to Aston Villa last month.
"I'm not interested in the speculation," he told Sky Sports after that match.
Sarri has told Chelsea he wants to return to Italy after one season in England and the club has said it will not stand in his way.
He had the option of another year on his contract, but never felt comfortable living and working in England and was frustrated he did not have a close relationship with the decision-makers at Chelsea.
Sarri's replacement will not be able to sign any new players, as things stand, with Chelsea having appealed against its two-window transfer ban imposed by FIFA to the Court of Arbitration for Sport (CAS).
The Europa League champion was sanctioned in February for breaching rules regarding the signing of under-18 foreign players, but was unsuccessful in its appeal to FIFA in May.