Cardiff manager Neil Warnock contacted his Dons counterpart Derek McInnes earlier this week to discuss the Irishman.
Now the Welsh side have followed up with an official approach.
But Aberdeen say the offer does not match their valuation of the 29-year-old Republic of Ireland international.
Hayes, who has another 18 months left on his contract, is currently with the rest of McInnes’ squad at their Dubai winter training camp.
Aberdeen said in a statement: “The club has confirmed that it received a bid late last night for winger Jonny Hayes from Cardiff City which has been rejected.”
Speaking to RedTV, McInnes added: “The bid fell way short of our valuation and that Jonny, as with all the squad, remains an integral part of the plans for the second half of the season.”