Jorginho played a key role in Napoli's unsuccessful title challenge last term, featuring 39 times across all competitions and scoring four goals.
Napoli president Aurelio De Laurentiis claimed in June that the Serie A club had turned down a €50million bid from City for the midfielder, but Pep Guardiola's side were expected to return with an improved offer.
And the drawn-out negotiations now appear to be nearing a conclusion, with Napoli confirming on Monday that the Brazil-born Italy international had not joined the squad for their pre-season training camp in Dimaro Folgarida.
The Blues had been hoping to bring him to the club ahead of the World Cup, but adjusted their expectations after Napoli rejected their initial proposal.
Jorginho recently spent some time with family in Brazil, his homeland, after learning that the deal had dragged on, but returned to Europe and is now ready to sign a five-year deal at the Etihad Stadium.
Initial squad list for pre-season training camp in Dimaro Folgarida:— Official SSC Napoli (@en_sscnapoli) July 2, 2018
Jorginho would become Guardiola's first signing of pre-season, as City look to defend their Premier League crown.