It had been claimed that Cesc Fabregas would leave Chelsea to go in the other direction, but these reports are apparently wide of the mark.
Former banker Sarri, 59, will be Chelsea's ninth full-time manager since Roman Abramovich bought the club in 2003.
Players such as David Luiz and Willian would have been moved on, though Chelsea were also concerned Eden Hazard might opt against signing a new long-term contract while Conte remained at the helm.
Conte - who had a year to run on his contract - is seen to have contributed to his own demise by falling out both with the players and the board as the sheen of the title victory quickly disappeared.
With Jorginho at his disposal, Sarri should be able to replicate most of that system from Napoli, which might help guide Chelsea back into the top four.
Barcelona sign €35m Lenglet from Sevilla
Barca now have four centre-backs in their ranks with Gerard Pique, Samuel Umtiti and Thomas Vermaelen. Sportsmail revealed last month that Chelsea had rejected a £50m offer from the Spanish side.
'It wasn't easy for me to convince you in the beginning but in the end I hope I did you proud!
In his first season in charge, Chelsea set a wins record with 30, finishing atop the Premier League table, comfortably ahead of Tottenham Hotspur in second place.
Before joining Chelsea, Conte had only coached in his native Italy, leading Juventus to three consecutive Serie A titles from 2012-14 before taking over the national team at Euro 2016.
The main reason for the prolonged saga has been compensation.
But The Sun say Chelsea are hopeful that, now Sarri is in charge, the trio will decide to stay at Stamford Bridge. Sarri could be joined by former Chelsea striker Gianfranco Zola as part of the backroom staff.
Sarri could be followed by midfielder Jorginho from Napoli, with Chelsea willing to pay £50m, plus £7m in bonuses, for the pair.
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