Manuel Pellegrini is believed to have set his sights on signing the 27-year-old, with reports in Spain suggesting a £21.2m deal had been agreed between the two clubs.
The FA Cup finalists are in the market for a striker having sold Carlos Tevez to Juventus, while a move for Napoli's Edinson Cavani has stalled in recent weeks with the Uruguayan favouring a move to Chelsea.
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"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."
Negredo himself, however, has admitted that he has not yet heard anything about a transfer.
"I'm taking advantage of the last few days of holiday I have left," he said. "The truth is that they haven't told me anything concrete. All I know is that I have to be in Sevilla on Saturday."
Meanwhile, Club president Jose Maria del Nido has virtually ruled Atletico out of the running for Negredo, saying they have "zero chance" of beating City to the Spain international's signature.
"I see Atletico’s chances of getting Negredo as very difficult," Del Nido told reporters.
"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."
Atletico had hoped to sign Negredo as a replacement for Radamel Falcao, who joined Monaco at the end of May, and manager Diego Simeone is afraid the club will lose ground if they cannot adequately replace the Colombian.
"Real Madrid have already got Isco for €30 million [£25m] and Barcelona have bought Neymar, while we have nobody. Nobody has arrived and that is difficult for me. We are looking at alternatives to become more competitive," he told Fox Sports.
"If we do not improve the squad all that we have achieved until now will be difficult to surpass. We still have not replaced Falcao and I hope that is resolved in the coming hours."