City were interested in the England international and were tipped to complete an £8 million move for him, but the 25-year-old, who signed a new four-and-a-half year contract with Villa in January, says he is staying put.
“I’m aware there has been intense media speculation surrounding my future in the last 24 hours and I want to set the record straight,” he said on the club’s official website.
“I’m not leaving. I’m staying at the football club and I can’t wait for the start of the season and captaining this great football club.”
Delph’s decision should represent a major boost to Villa manager Tim Sherwood, who appointed the midfielder captain.