The clubs have been negotiating for a number of weeks now, but this is the clearest indicator yet that the player will indeed be playing his football at the Etihad Stadium next season. The club are said to have increased their latest offer to £53m in total.
City have been chasing him following a tremendous season over in Serie A, where he helped push Napoli's title charge all the way with Juventus. The 26-year-old scored two goals and had four assists in 33 matches for I Ciucciarelli.
The Italy international drew many plaudits for his excellent control of games from midfield and fantastic range of passing.
He was a player identified pretty early on by manager Pep Guardiola as someone who could perhaps replace Fernandinho in seasons to come, and now Napoli president Aurelio De Laurentiis has revealed the two parties have almost completed a deal.
Speaking to the Sun, De Laurentiis said: "I think the deal can be done in the next few days. Everything is possible as we have a good relationship with Manchester City and their people but we must negotiate.
"We are still not in agreement over the price for the player but we'll be near to the conclusion as they made an effort in the last few days."
Napoli are reportedly lining up a move for Sampdoria star Lucas Torreira as Jorginho's replacement but face competition from Arsenal, who are eyeing his £22m release clause.