"We have received an offer from Manchester City for James Milner and this has been firmly rejected," said a Villa spokesman late on Wednesday.
"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."
The 24-year-old midfielder was recently named PFA Young Player of the Year.
Leeds-born Milner, who joined Villa from Newcastle for £12m in 2008, is halfway through a four-year deal.
Villa owner Randy Lerner said last week the club will do "everything" in their power to ensure Milner stays.
Premier League and FA Cup Double winners Chelsea and Manchester United have also been linked with Milner, though United boss Sir Alex Ferguson has talked of this summer's transfer market as being "very difficult".
606: DEBATE
Milner reminds me of Tevez in midfield - works hard, never gives up, great attitude. Just the type of player we need
Ananee
Villa have secured Europa Cup football for next season having finished runners-up to Manchester United in the Carling Cup final and will not want to lose another influential midfielder to City following the departure of Gareth Barry for £12m last season.
City, funded by the deep pockets of Abu Dhabi-based owner Sheikh Mansour Bin Zayed Al Nahyan, are close to signing Germany international defender Jerome Boateng from Hamburg for £11m.
More signings are expected this summer as City push for a coveted Champions League spot having just missed out to Tottenham this season.
Milner has been in a rich vein of form this season, helping Villa finish sixth in the Premier League and reach the semi-finals of the FA Cup, since O'Neill switched him from wide midfield to a more central position.
He has also become a regular in the England squad under Fabio Capello, and is widely tipped to be part of the 23-man squad for the World Cup in South Africa.
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Im confident we will get him but will cost around £22-25m - way over the top imo for him like when we paid £24m for Lescott but we can afford it and he is a class player. Or we might include SWP or Onuoha in a deal plus £20m. Boateng will be £11m which i think will be a very good deal.