City kick off their pre-season on Monday July 4, and the English outlet claim that Pep Guardiola is hopeful of securing a deal for the midfielder before the camp begins.
The club have been in negotiations with Napoli for a while now, as they attempt to bring in a man who is seen as a replacement for the departing Yaya Toure, and it appears talks are nearing a conclusion.
The aforementioned outlet state that City will pay a fee in the region of £43m for the 26-year-old, who hails from Italy.
The defensive midfielder has attracted attention from various big European sides after an impressive season with Napoli, who came close to beating Juventus to the Serie A title. Jorginho played in 33 of the Italian side's league games, contributing two goals and four assists from a deep midfield role.