The Rojiblancos were showing considerable interest in the 27-year old but admit they cannot compete with the reported £21.2million offer made by City who are backed by UAE petroleum magnate Sheikh Mansour.
"We can't compete with the petrodollars," an Atletico spokesman told orgulldenervion.
"We're speaking but we won't be able to reach the amount Manchester City can offer."
Sevilla president Jose Maria del Nido added: "I see Atletico’s chances of getting Negredo as very difficult.
"In fact, as of today [Wednesday], they have a zero per cent chance. We have had no contact with them for the last 10 days.
"There have already been major offers from various other teams that I have rejected."