The Blues have been very inactive in the transfer window so far due to the uncertainty surrounding the club's leadership, but with Sarri set to replace Antonio Conte they can finally crack on with a squad overhaul.
Sarri is set to utilise his Napoli links to bring Jorginho with him to Stamford Bridge, and there have also been suggestions that he could sign Gonzalo Higuain from Juventus. Sarri and Higuain worked together at Napoli.
Zappacosta could go the other way though as the Daily Star reports that the Italian is set for a £20m switch to the Stadio San Paolo.
The 26-year-old joined from Torino for £23m last summer but has failed to make an impact at Stamford Bridge, with many of his 22 Premier League appearances last season coming as a substitute.
He also made a handful of appearances in cup competitions, but scored just two goals and provided only two assists in what was a very disappointing campaign for Chelsea.
New rules prohibit English clubs from completing new signings after August 9, but they can continue to sell players to foreign clubs until the end of that month.