Liverpool have been tracking the Algerian international for some time and had been hoping to pick up a bargain, with the player's contract set to expite next summer.
However, reports in France now claim that Jurgen Klopp's side face competition from City, who are on the lookout for a replacement for Benajmin Mendy, who is facing a lengthy spell on the sidelines after picking up a serious knee injury against Crystal Palace.
The agent of fellow Napoli defender Mario Rui recently gave hope to Ghoulam's suitors, by suggesting that the 26-year-old would not sign a new contract in Naples.
'I don't think Ghoulam will renew with Napoli, and it's enough to think that in four months he'll be able to sign for whoever he wants for nothing,' he explained.
'He could earn €5m and if I were his agent I'd do that, and I don't think the others are stupid. I don't believe these stories that Ghoulam wants to renew, if he wanted to renew he'd already have done it.
'Besides, with the way he's playing Napoli can't afford to put him in the stands. After August 31, it's the player who has the handle of the knife.'
Napoli boss Maurizio Sarri is thought to be relutant to allow Ghoulam to leave, with the defneder undoubtedly one of his best players but given his contract situation, the player holds all the cards.
Both sides would be able to open talks over a bosman move for the defender in January, though City may test Napoli's resolve with a cash offer as they look to fill the void created by Mendy's untimely injury.