Sarri was brought in as the Blues' new manager last summer and led them to a third-placed finish in the Premier League. There is no desire at the club to bankroll Sarri's departure.
Sarri's future at Chelsea has been the subject of intense speculation for most of this season and a decision is expected to be made on the Italian one way or another after next week's Europa League final against Arsenal.
Yet according to The Metro, the Blues could face a mass player exodus if they decide to stick with Sarri in 2019/20.
Sarri led Chelsea to third place in the Premier League and the League Cup final this season, and is now preparing his side for the Europa League final against Arsenal on May 29.More news: North Korea: Joe Biden is a 'fool of low IQ'
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Lampard has impressed in his first season in management, leading Derby to the Championship play-off final against Aston Villa on Monday, live on Sky Sports Football.
"These rumours have seen Frank Lampard backed into the 4/5 favourite to replace Sarri should the Italian leave this summer and the former Chelsea midfielder is the only name on punter's lips at the moment".
The Blues have been slapped with a two-window transfer ban but still hope they can successfully appeal the suspension.
"In Kovacic's case, a move is already being explored and a fee could be agreed to convert his current loan into a permanent deal without a need for Chelsea to re-register the player on the electronic TMS system used to process transfers".