The News of the World says the European giants will take advantage of the FIFA ruling enabling them to sign the Manchester United star in 2010 for the remaining two years of his salary - around £10million.
And that puts pressure on United to complete new contract talks to keep Ronaldo at the club until 2014 and increase his wage to £140,000 a week.
Reports in Spain and Italy are indicating that both Real and AC Milan will try to trigger the FIFA regulation to snap up the Portuguese winger, who has emerged as the hottest property in the world after his record-breaking season.
United boss Sir Alex Ferguson, however, maintains: "We get used to it. It's their way of tapping up a player. Of course UEFA don't do anything. There is no point. We just get on with it.
"Ronaldo loves it here. This is his place."