The Italy international has been heavily tipped to join the Premier League champions in the transfer window, although Liverpool, Arsenal and Chelsea are said to be providing competition.
A report from Calcio Napoli 24 on Wednesday claimed City have agreed a deal with the 26-year-old that could cost the club as much as €50 million (£44m/$58m).
Joao Santos claims an offer has been made to Napoli and admits it would be hard to turn down City's advances.
"If Napoli find an agreement with City, we will assess everything.
"Obviously, Manchester City would be very welcome, an opportunity not to be turned down. The coach is one of the best in Europe."
Jorginho has established himself as one of Serie A's finest midfielders since signing from Verona in 2014.
He made 33 Serie A appearances in 2017-18, scoring twice.