According to Il Mattino, the English club have offered €73m for Koulibaly, 29, but Napoli have yet to accept.
Koulibaly’s agent, Fali Ramadani, knows he cannot present an ultimatum in the way City want.
Ramadani fears that the notoriously difficult Aurelio De Laurentiis, Napoli’s owner, could call off negotiations or make things even more complicated.
Koulibaly is settled in Naples and earns €6m-per-season, so it would be no drama for him to stay.
Pep Guardiola wants Koulibaly as his second centre-back signing following the arrival of Nathan Ake from Bournemouth.
However, if talks with Napoli continue to drag on, the City boss is likely to turn to other options.