The Spaniard had also said that he would never manage any other club in England, but did a U-turn and took over as the interim manager of Chelsea in 2012.
Sarri used to coach Empoli and the Serie A side's president, Corsi, has opened up on his contact with the still Chelsea manager.
With the transfer embargo now in place at Chelsea they will be looking to retain more of the players they allowed out on loan last season and it is thought that the 20-year-old will be in and around the Blues first team squad for the 2019/20 campaign.
Frank Lampard and Derby tasted defeat in the playoff final. However, he was largely not very popular at Stamford Bridge and struggled to win over support from fans of the club.
At the moment, Chelsea are yet to make an official approach to Derby, with Lampard, alongside his assistant Jody Morris, are the fans' top choice to take over from Sarri.
Asked whether Lampard would be ready for the job after one season in the Championship with Derby, Drogba said: "Does he have to wait until he is 40 or 50 to be ready? I work and try not to think about these things". You want to know who your first game of the season is against - I think that's the first one you look out for.
"They have tried with all these great managers".
The west London club are refusing to budge and won't let him leave for Italy until a compensation package has been agreed. But they have got to be given time. "It is not because Frank lacks experience, it will mainly be because they have lost their best players".
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