The next manager will be presented with new signings despite the massive outlay by Perez last summer.
The president is a known fan of Rooney and went on record after Euro 2004 to state his admiration for the striker when he was trying to gain election to office for a second time.
He said of the then Everton player: "Rooney has shown at Euro 2004 that at the age of 18 he is a splendid player and that he is mature enough to develop to become the most important player in the world.
"If [Real coach Jose Antonio] Camacho tells me he would like Rooney, I will do my best to sign him."
There are doubts about Rooney's ability to settle in Spain, though, and whether he would be able to learn the language as well as previous English imports Steve McManaman and Jonathan Woodgate.
Real are also desperate for a creative midfielder and left-back and Gerrard - who may feel it is time to leave Liverpool if they fail to win a trophy this season - and Clichy may be more realistic targets.
United boss Sir Alex Ferguson would also resist the sale of his 24-year-old talisman after sanctioning Ronaldo's exit last summer.
But with United currently more than £700m in debt under the ownership of the Glazers, Rooney may have to go if they receive an offer they cannot refuse. And there has been talk of a new contract for the striker for several months but nothing has been signed.
For the time being, Rooney is just focusing on leading United back to the Champions League Final in Madrid.
"The team are playing well and I'm scoring so I'm very happy," he said. "I'm playing the best football of my career at the moment.
"I'm delighted to get up to 30 goals and hopefully I can kick on from here and try and get more."
