Wayne Rooney ready to make U-turn over Manchester United exit following appointment of David Moyes

Wayne Rooney is prepared to consider staying at Manchester United under David Moyes, who has been appointed manager on a remarkable six-year deal, but having made his second request to leave in three years he will find the odds stacked against him in his attempts to win over supporters and Sir Alex Ferguson's successor.

Rooney tried to repair the damage he had done by libelling Moyes in his 2006 autobiography by making a telephone apology to him four years ago and the player, who made a verbal request to leave United two weeks ago, is open-minded about the idea of working again with his old Everton manager.

The forward's desire for a fresh start has accrued from a problem with Ferguson, who has dropped him out of United's strike force, rather than with the club. Though Moyes will not take up his new position until 1 July, the two are likely to talk almost immediately.

Rooney, who has two years to run on his current contract, is understood to welcome the chance to speak to the manager who gave him his Premier League debut in 2002.

Though the prospect of Cristiano Ronaldo returning to United might appeal to Rooney, the move seems unlikely, with the Portuguese understood to want a season free of Jose Mourinho at the Bernabeu Stadium before any possible dramatic return to Old Trafford.

When Ronaldo celebrated scoring his 200th goal for Real Madrid in 197 appearances on Wednesday, he thumped the club badge on his shirt and pointed to the pitch beneath him and appeared to shout: "I'm here, I'm here." There was also what appeared to be an insult directed at the home dugout – and Mourinho.

Reports in Spain tonight suggested Radamel Falcao had chosen Monaco over Chelsea with the Ligue 1 club the only side prepared to meet his €60m (£50.6m) buy-out clause and his €10m (£8.4m) wage demands. That may make Rooney a Chelsea target.

Whether too much should be read into some mid-match passion from Ronaldo, and whether "I'm here" is the same as "I'm staying here" is debatable but those close to the winger say he wants the opportunity next season to show that Real Madrid's recent success – three straight semi-final appearances in the Champions League following six seasons without getting beyond the last 16 – has been more about his contribution than his manager's. The relationship with Mourinho has never matched the one he enjoyed with Ferguson, to whom Ronaldo paid tribute this week, saying, "Thanks for everything, boss", after news that the Scot had retired.

United have no former players lined up to make an event of Sunday's emotional last home match for Ferguson, against Swansea City, as there has not been time following the conclusion of discussions with Moyes, which resulted in the announcement of his appointment. The six-year deal is a remarkable statement of belief in the new manager, with the decision to delay its start until July taken to fall in line with most other contracts at the club, according to sources.

Ferguson, who met his players today, said in that announcement that Moyes was "a man of great integrity with a strong work ethic. I've admired his work for a long time and approached him as far back as 1998 to discuss the position of assistant manager here. He was a young man then at the start of his career and has since gone on to do a magnificent job at Everton."

Moyes said: "I know how hard it will be to follow the best manager ever, but the opportunity to manage Manchester United isn't something that comes around very often."

He was in contention for United's assistant manager job after Brian Kidd left for Blackburn Rovers. Ferguson asked chief scout Les Kershaw and former youth coach Eric Harrison to put out feelers and find the best up-and-coming managerial talent in football. After two months they recommended Steve McClaren (then deputy to Jim Smith at Derby), with Moyes as reserve. McClaren was known for being an even greater student than Kidd of foreign methods, so Ferguson went for him.

Ferguson was so convinced that McClaren was his man that there is not even reference to Moyes in his autobiography Managing My Life.