The Italy international's agent has held successful talks with City's director of football, Txiki Begiristain, and a deal is not far off, according to journalist Jose Alvarez Haya:
Jorginho has played a key role in Napoli's title challenge this season. Maurizio Sarri's side beat leaders Juventus 1-0 on Sunday to close to within just a point of top spot with four games remaining.
The midfielder has spoken previously about reported interest from City and seemed flattered by the links with Pep Guardiola's team, as shown by ESPN FC's Jonathan Smith:
The Napoli star looks a good fit for the Premier League champions. He's an accomplished deep-lying playmaker who is superb in possession.
As well as being a wonderful passer of the ball, he can also dictate play and start attacks from deep. Sarri's side have lit up Serie A playing superb football, and it's easy to see why Guardiola may be tempted by the 26-year-old.
Ted Knutson at StatsBomb explained why Jorginho moving to City would make a lot of sense:
Jorginho's agent, Joao Santos, has said he is happy at Napoli but that he plans to talk to the club "about his contract situation at the end of the season," per RMC Sport (h/t Football Italia).
City could face competition for Jorginho as rivals Manchester United have made him one of their priority targets, per Miguel Delaney at The Independent. Liverpool are also interested in him as a potential replacement for Emre Can, per David Maddock at the Mirror.
However, Jorginho's comments about Guardiola suggest City may well be his preferred destination, and interest from the Premier League champions is sure to be tempting.
If he were to move to City, it would be bad news for the rest of the top flight. Guardiola's side cantered to the title this season, and further strengthening their team is likely to extend their domestic dominance.
It was a different story in Europe as City were knocked out of the UEFA Champions League by Liverpool at the quarter-final stage. Guardiola will want to improve on that next season, and he may feel he needs to add further quality if he is to bring the European Cup to City for the first time in their history.