Rooney sparked rumours of a United exit last week when he contradicted manager Sir Alex Ferguson's claims that he had an ankle injury, and it is understood he is now refusing to discuss a contract extension.
Rooney, 24, has little more than 20 months to run on his current deal and amid claims he United could cash in the club took the unusual step of dismissing the stories - "To suggest Wayne Rooney will be sold in January is nonsense," a spokesman said - but the reports have intensified.
Ferguson is finalising his plans for a response to the eruption around Rooney, which is expected to be delivered on Tuesday, but Mourinho, whose team have been put at the head of the queue to sign the England international, expects him to stay.
"I don't think he will (become available)," Mourinho said ahead of Real's Champions League clash with AC Milan. "I think the big man will persuade him to stay."
Amid the furore, Real Madrid's director general, Jorge Valdano, confirmed his admiration for Rooney but suggested there may be no place for him in the current team.
Valdano told Telemadrid: "I really like Llorente and Rooney, too, but the question is, if Rooney comes, who do we take out of the team? We have a brilliant strikeforce in Ronaldo and Higuain and now we have added Ozil and Di Maria to complement them."
Ferguson will doubtless be questioned on the Rooney issue on Tuesday when he is due to attend a press conference ahead of United's Champions League encounter with Turkish champions Bursaspor.
Rooney's future has been a hot topic with Europe's big hitters during Monday's pre-match press conferences and Chelsea manager Carlo Ancelotti refused to be drawn on whether the Blues would show an interest in the striker.
"I cannot really give an answer about this," Ancelotti said. "Rooney is a Manchester United player and he has some problem at this moment but the club has experience and when a big team has top players like Rooney, they want to keep him in the squad."
Manchester City, who lured striker Carlos Tevez from cross-city rivals United in July 2009, have also already been linked with a big money move for Rooney.
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This post has been edited by 14. on 19 Oct 2010, 01:47