Both Chelsea and Juventus announced the news simultaneously with the Blues' general manager Marina Granovskaia explaining that Sarri had: "made it clear that he wanted to return to his native country, explaining that the reasons for him wanting to work in Italy were important".
Chelsea said in a statement they had terminated Sarri's contract with two years to run at the Italian's request.
According to The Daily Mail, via Sky Sports, Hudson-Odoi is willing to commit his long-term future to Chelsea if they go with Lampard as Maurizio Sarri's replacement.
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Sarri won the Europa League in his final Chelsea match and led the club to third place in the Premier League.
And from today, he will take over the reins at Juventus with a contract until June 30, 2022. The Blues also reached the Carabao Cup final, losing out to Manchester City.
The Europa League win last month was Sarri's first major trophy as a coach, but he will be expected to deliver far more in Turin.
But Derby are keen to extend Lampard's deal - which has two years left - and have opened talks with the 40-year-old.