The Serie A club, emboldened by their recent US takeover and with new coach Luis Enrique in place, are understood to have offered a fee close to the £6.5million (Dh38.5m) City spent acquiring the Argentina international three summers ago.
Zabaleta has been a consistent member of Roberto Mancini's starting lineup at City, valued for his athleticism, attitude, and a tactical intelligence that enables him to play in either full back position and all across the midfield.
The 26 year old agreed a four-and-a-half-year contract extension in December 2009, and City are expected to reject Roma's
Roma's summer transfer activity is being led by Franco Baldini, the England national team's 'general manager'.
Fabio Capello's deputy has told journalists he is doing the work in his spare time, but is preparing to formally return to Italian football once he has negotiated an exit from his England's duties.
Zabaleta has also drawn the interest of Malaga, the Spanish club recently purchased by Qatari royal Sheikh Abdullah Al Thani.