The 32 year-old Uruguay international made the revelation when discussing his future with Atletico.
"I was looked at by Manchester City, but I preferred to stay here to prioritise other aspects," Godin told El Larguero.
But Godin does not want to close the door on a future move.
"I work for the day and never intend to stop. I do not see myself in another Spanish club's shirt, but never say never."