Jorginho, 26, had appeared to be closing in on a switch to the Etihad Stadium following weeks of discussions between the two clubs.
City had an initial offer of £44m rejected by Napoli, but they were expected to return with a slightly improved bid and the player was keen on a switch.
Chelsea, soon to be managed by ex-Napoli boss Maurizio Sarri, have emerged as late contenders to nab the Italy international, however, and the Blues are now the frontrunners to get a deal over the line.
Speaking on Wednesday morning, Partenopei chief De Laurentiis said: “We said to ourselves, ‘if Jorginho has any requests, we’ll take them into account’.
“For that, I’ll have to apologise to Manchester City. However, if the player would rather live in London than Manchester, I can understand that.
“If Chelsea are paying him even more, I can understand that too. Jorginho and Sarri together again? Jorginho would go to Chelsea regardless of Sarri.”
Jorginho is reportedly heading to London on Wednesday to discuss personal terms with Chelsea.