Manager Roberto Mancini admitted Manchester City have given up on signing Robin van Persie after expressing his frustration with the club's transfer policy.
Both City and derby rivals United have lodged bids for the Arsenal striker, who is in the last year of his contract and has refused to sign a new deal.
But with the transfer window closing in just three weeks' time, Mancini feels negotiations have hit a dead end.
"We only have 20 days to the end of the market and I don't think that we have any chance for him," he said.
Mancini said two weeks ago that City would need to improve their squad if they are to retain the Premier League title this season.
Football administrator Brian Marwood is responsible for player recruitment and Mancini put pressure on the former Arsenal player by saying he hopes "he can do a good job" in securing his transfer targets.
City have been linked with the likes of Daniel Agger, Scott Sinclair and Daniele De Rossi yet with the Blues set to face Chelsea in the Community Shield on Sunday, they remain the only Premier League side yet to sign anyone this summer.
Asked whether he was happy with the management structure at City, Mancini replied: "I am not happy - but I don't know what to say.
"You need to ask Brian Marwood," he added. "I am not the sporting director. I can't say anything about players."