The 31-year-old is expected to leave the Etihad this summer as he moves into the final 12 months of his contract.
Several sides in Italy have shown an interest, including Inter Milan and Roma, while Zabaleta has also been offered the chance to return to Argentina.
However, according to Corriere dello Sport, the right-back is closing in on a move to Roma after agreeing personal terms with the Italian club.
The Argentina international has provisionally agreed to sign a three-year deal worth around £40,000-a-week.
Roma will now hold talks with Manchester City on Tuesday to try and agree a fee of around £2million for the defender.