The 34-year-old Argentinian midfielder revealed that new City boss Roberto Mancini, whom he played with at Inter Milan, had offered him a deal at Eastlands but he rejected the offer in favour of staying with Estudiantes.
"I presented the offer to the directors of the club (Estudiantes) so they could consider it, maybe it appeals to them," Veron told radio station La Red.
"For my part there isn't much thinking to do, my (negative) answer was instantaneous.
"It's not possible at the moment and it's not a question of money. My family and my affections are involved.
"I took a decision and I want to respect it. I can't leave, I'd be going against my convictions, I'd be letting myself and the fans down above all else,"