That would more than likely mean allowing Villa, the 27-year-old Spain international, to leave despite signing a new six-year deal last August, with City believed to be in pole position after making an inquiry about a move in the last transfer window.
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Valencia vice-president Fernando Gomez said: "It's true we spoke with them but they didn't make us any offer. The President, Vicente Soriano, asked for a significant amount and they didn't agree."
Villa has always made it clear he would much rather stay in Spain than move to any of his Premier League suitors and any move, should an English club manage to overcome the player's reluctance, would involve a fee of more than £40 million.
Gomez did not specify a fee for either Villa or his Spanish international team-mate David Silva – a long-term target of both Liverpool and Manchester United – but insisted they would make sure Valencia received the best possible price for both.
He said: "They are two very important players with a lot of quality, and we are not going to sell them on the cheap.
"I would like them both to stay but we cannot discount anything and any of the players could leave at the end of the season."