The Colombian veteran, who has been plying his trade at San Siro since 1999, was tipped last year to work again with manager Roberto Mancini at City.
For a while the idea of playing under Mancini, who was in charge of Inter from 2004 till 2008, appealed to Cordoba but he eventually decided to stay put.
After a the Nerazzurri revelled in an unprecedented treble last season, the 34-year-old felt glad he snubbed the Citizens despite the fact that he could have played more first team-football in Manchester.
"I was going through a tough period at Inter, I really wanted to play football because I was feeling in great shape," Cordoba told Inter Channel.
"I had the chance to join Manchester City last season, but I agreed with the club and the coach that I would stay to give a helping hand to this side – as I always have done.
"I continued at Inter and I am proud that I did. I want to thank all of those who helped me make the right decision.
"To not have been at Inter after everything that we won last term would have been a real shame."