Valencia sporting director Miguel Angel Ruiz spent three days trying to persuade Everton to sell Arteta and made a £15m offer.
But Everton's hierarchy dismissed the offer out of hand and told Valencia they would be reluctant to sell even for £25m.
Valencia were also ready to offer ex-Everton and Portsmouth midfielder Manuel Fernandes as part of the deal - but that was rejected as well.
"The sort of money Everton wanted was impossible for us and showed that they are not interested in any kind of deal," said Ruiz.
Arteta's agent Inaki Ibanez added: "I am aware of the interest, but any deal is down to Everton and whether they want to sell but the player is also very happy and does not want to leave England."
