City, thanks to their mega-rich owners, are one of few clubs in the world with deep enough resources to buy Rooney, or afford his wages.
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City coach Roberto Mancini said he has had no contact with United about bringing their unsettled forward across to the blue half of the city and many fans are hoping it stays that way.
"We don't need to spend anymore, we need this team to settle," Jacqui Grant, who was shopping in central Manchester wearing a City sweatshirt, told Reuters on Wednesday.
The world's richest club have spent more than 300 million pounds building a team since being taken over two years ago, bringing in the likes of forwards Emmanuel Adebayor, David Silva and ex-United striker Carlos Tevez.
"Rooney shouldn't come to City, we got away with it with Tevez, but this could cause a lot of trouble, a lot of unrest in the city of Manchester," added Grant.
"I don't like him as a guy, he can't play at the moment, he had a bad World Cup, he's not going to help us."
Her 16-year-old daughter Beth is a United fan and even she did not want Rooney to stay at Old Trafford after a poor start to the season.
"He's rubbish, nobody wants him. He should play in the reserves after saying he wants to leave. I won't be cheering him if he wears the shirt for the first team," she said.
"What's the point in buying an out of form player with personal problems for what will probably end up being a record transfer fee?" said office worker Paul Davis. "We don't want him and we don't need him."
After a miserable World Cup as well as allegations about his private life splashed across the newspapers week after week, Rooney's stock has fallen although his class is not in question after a 34-goal season last year.
"He's not as good a player as last season. He thought he was bigger than the club and that doesn't work here," said Pedro, a United fan who declined to give his second name as he walked past Old Trafford heading for a few pre-match drinks before Wednesday's Champions League match against Bursaspor.
"He has played himself into a transfer that he wanted - he's been putting in some dreadful performances this year.
"Sir Alex Ferguson is right not to let him get away with it. It all goes a way to explaining our start to the season."
Amid all the talk of Rooney heading for the Old Trafford exit, there were a few fans who think it will not come to that.
"I don't think he will leave," said Samuele Omiecceoli, who had flown from his home in Italy to watch Wednesday's game.
"He will stay at United because many times there have been offers from big clubs like Real Madrid and he hasn't gone."
