The News of the World says the Portuguese superstar's agent Jorge Mendes is in daily contact with Real sporting director Pedrag Mijatovic.
The deal would mirror the one negotiated by David Beckham when he left United for Madrid five years ago.
It would mean that, with his wages, Ronaldo would be earning £19.8m a year.
A source close to the Ronaldo negotiations said: "A move to Real would send his earnings rocketing.
"The Spanish club would offer him a much bigger platform to launch himself as the world's best and biggest football superstar.
"Markets would open up in the Far East in the same way they did for Beckham."
Spanish sources claim that Ronaldo, 23, has already chosen a property in Morajela, close to where Calderon and head coach Bernd Schuster both live.