City’s opening gambit was €63m plus bonuses, considerably less than the €70m-plus Napoli want.
The Citizens are determined to sign Koulibaly, 29, and will try again after the Champions League ends.
Contacts are being kept alive by the player’s agent, Fali Ramadani, who is playing an important role.
Relations between City and Napoli are not good after talks for Jorginho led to him joining Chelsea in 2018.
Pedulla adds that other clubs entering the Koulibaly race can’t be ruled out, with Manchester United known admirers.
However, if talks with City drag, they could risk losing Gabriel, who has several English teams on his case.