Valencia are in financial trouble and have conceded they may have to sell Villa to ease their concerns.
The 27-year-old was a key member of the Spain squad that triumphed at Euro 2008 and is Valencia's most valuable asset.
Vice-president Fernando Gomez told Spanish radio station Cadena Ser that the player would cost a "significant amount".
When Gomez was asked if Valencia chiefs had met with two representatives from Manchester City regarding the sale of Villa, he added: "Yes, it's true but they didn't make us any offer.
"The president Vicente Soriano asked for a significant amount and they didn't agree," he said.
No price tag was revealed but Gomez did confirm that despite Valencia's precarious financial predicament, Villa and fellow Spain star David Silva would not be allowed to go for a reduced price.
"I think they are two very important players, with a lot of quality and if we sell them, we are not going to sell them on the cheap," stated Gomez.
"I would like them both to stay but we cannot discard anything and any of them [the players] could leave at the end of the season."
The skilful Villa has been a target for other Premier League clubs, with Liverpool and Chelsea both linked to bids in recent seasons.
In January, Manchester City failed in a bid to take AC Milan's Brazilian playmaker Kaka to Eastlands and also recently denied rumours linking them to Barcelona forward Lionel Messi.
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