Cordoba was strongly linked with a move to City in the January transfer window.
He told Inter Channel: “I was close to leaving Inter. There was a difficult period for me, I wanted so much to play because I felt in good form.
“I had the chance to go to Manchester City last season, but I agreed with the club and the coach to continue to lend a hand to this team, as I always do and I am proud to have done it.”
“I thank those who helped me to make the best decision. Leaving Inter last season in which we carried many victories would have been a pity,” Cordoba added.