Mancini's side have been installed as favourites to sign Rooney after Tuesday's revelation that the striker - whose current deal expires at the end of the 2011/12 season -
wishes to leave United.
But in the press conference ahead of his team's Europa League home match against Polish side Lech Poznan on Thursday, Mancini echoed the comments of Jose Mourinho - whose Real Madrid side have also been linked with the player - when he said he expected Rooney to stay at United.
"He is an important player for United and I think he will stay," added Mancini. "I have respect for him, for Ferguson, for United. I want to speak only about my players."
Despite his belief that Rooney will remain at Old Trafford, Mourinho admitted that he admires Rooney and that he would be interested in signing him if he was to become available.
"He probably wants to leave for some reason but I believe he belongs to Man United, he belongs to Man United fans, he belongs to Old Trafford," Mourinho told Sky Sports after
Real's 2-0 win over AC Milan
in the Champions League on Tuesday.
Ferguson confirms Rooney rumours in dramatic media conference
"But if at the end of day, Man Utd decides that he is to leave, give me a call."
Premier League champions Chelsea and Real's Spanish rivals Barcelona are two other clubs believed to be among the front-runners for Rooney's signature.
"I don't want other coaches talking about my players and I have a lot of respect for Manchester United and their manager Alex Ferguson that prevents me from discussing Rooney's situation," he said.
But Blues striker Nicolas Anelka was more forthcoming, admitting that should Rooney wish to join Chelsea, he would be "welcome".
Ferguson stunned observers by laying bare the fall-out with his star striker at an extraordinary media conference on Tuesday.
English newspapers reported
the manager had put across a feeling of betrayal that posed the question whether Rooney had put loyalty to his club above money.
'Roo's let Utd down,' said a headline in the Sun, while the Daily Mirror's simply read: 'Betrayal'.
The Guardian added that Ferguson's speech "nailed several myths and cast Rooney as a mercenary with no regard for United's health".
But it is understood Rooney is privately saying it is ambition, and not riches, that is driving his thinking.
Ferguson said he was bemused, shocked and disappointed that Rooney wants to leave.
"It's disappointing because we have done everything we possibly can to help Wayne Rooney ever since he came to the club," said the Scot.
Former Manchester United favourite Sammy McIlroy admitted to being "baffled" by Rooney's decision and warned of the potential pitfalls of a move to Manchester City.
"Wayne Rooney has been an absolute idol over the past few years for Manchester United fans," McIlroy told BBC Radio 5 live. "If Wayne think he's in a bit of a goldfish bowl at the moment, if he goes just across the town it will be even bigger.
"Maybe Wayne thinks he needs a change, but to go just across the town, he could be in for a rough ride.
"There will be a lot of United fans hoping he changes his mind and Sir Alex will be hoping he changes his mind as well but these days money talks."
United supporters are concerned their team will find it hard to replace a man who scored 34 goals last season, citing what they perceive as the club owners' lack of ambition.
"The question being asked by many fans is does the ambition of the owners match that of Rooney or indeed supporters?" said a spokesman for the Manchester United Supporters' Trust (Must).
"On the evidence so far it would appear the answer is clearly not."
Must, which has strong links to the Red Knights group that wants to buy the club, is set to hold another protest against the club's owners before the match against Tottenham on 30 October.
The Glazer family, led by Malcolm Glazer, became owners of the club in 2005 to the anger of many United fans.
The majority of the cash used by Glazer to buy the club is understood to have come in the form of loans, much of which have been secured against the club's assets. United reported an
annual pre-tax loss of £79.6m
earlier in October.
Former Manchester United and Inter Milan midfielder Paul Ince has suggested a move away from England could be just what Rooney needs.
"With all the off-field antics going on it has all come down on him at once," said Ince, who spent two seasons in Milan. "Maybe he feels that the best thing for him to do is to move on and go to another country and start a new life.
"When I left Manchester United for Inter Milan it was the best thing that I could have done, to be away from everyone and concentrate on my family and my football. Maybe Wayne's thinking that."
Meanwhile, Tottenham manager Harry Redknapp has not ruled out a move for Rooney and revealed he will "talk to his chairman" about the possibility of signing him.
"If he's going to stay in England, who knows?" he commented. "You've got to be interested when the very, very best players become available but it would be a big ask.
"I'm sure there'll be some big fish out there wanting to take Rooney, that's for sure. He's a fantastic player - he's having a bad spell, he's had a bad two or three months - but he's a great player.
"One thing's for sure, he won't find a better club than Man United to play for. He's got a great manager there.
"I don't know what's gone on there but it's a shame if it ends that way."
Arsenal manager Arsene Wenger also jokingly asked "Has somebody opened the transfer window?" when he was questioned about Rooney.
He added: "We are not in the transfer market at the moment and we are not interested in buying anybody. We have plenty of players.
"It's a story I'm happy to read in the newspapers but I'm happy to keep out of it. That means we are not buying anybody, we have enough strikers."
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