The 24-year-old has become a key player at Villa Park since joining the club from Newcastle for £12million in 2008.
The England international is halfway through a four-year deal at Aston Villa.
A Villa spokesman said: “We have received an offer from Manchester City for James Milner and this has been firmly rejected.
“We plan to sit down with James and his representative after the World Cup to agree a new long-term deal and this remains our position.”
