It is understood Milan’s new sporting director, Leonardo, had a series opened talks over a deal for striker Alvaro Morata.
Morata joined Chelsea last summer from Real Madrid for an initial £57m, with the job of replacing Diego Costa.
But the forward scored just 11 goals in 31 Premier League appearances and lost his place to Olivier Giroud in the latter part of last season.
Sarri wants to bring in Juventus star Gonzalo Higuain, having worked with the Argentine at Napoli.
Sky Sports reports that their willingness to sell Morata, Chelsea will not let him go on the cheap and have placed a price tag of £62m on the forward.
Chelsea have already made initial contact with Juventus with the hope of signing Higuain, according to Sky in Italy.
Higuain scored 36 goals in 35 games for Napoli in in the 2015/16 season under Maurizio Sarri, who is now in charge of Chelsea.
Milan, though, are already facing scrutiny over their £200m spending spree last summer and are unlikely to have the means to stretch to Chelsea’s valuation.
Morata’s future is likely to depend on Chelsea’s chances of signing Higuain in the next fortnight but the Blues know Juventus are keen to sell having spent £99m on Cristiano Ronaldo. Hope Chelsea will be patience to void the mistake of Mohamed Salah.