It was understood that Delph had been in talks with Manuel Pellegrini’s side over an £8m move, but he will now be staying put.
In a statement on the Aston Villa web site, the midfielder said: “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.
“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 enjoyed an impressive season for Aston Villa last term, earning six England caps despite the club’s battle against relegation.
He moved to Villa Park from Leeds in 2009 after making 52 appearances for the Yorkshire club, and returned to Elland Road for a loan spell in 2012 after struggling to break into Villa’s first team.
But he has since gone from strength to strength despite Villa’s troubles, scoring eight goals in more than 100 appearances for the West Midlands club.