The Sunday Mirror says Ronaldo scored 53 goals last season - including the winner against Barca in the Copa del Rey final last month.
But that remains the only trophy he has won in the all-white kit of his boyhood idols.
Reports in Spain suggest that Ronaldo has become disillusioned with the tactics of Jose Mourinho and that Real were ready to cash in for £150m.
Only Manchester City would be able to meet such a valuation - but club officials were quick to dismiss claims of a move for Ronaldo last month.
Real Madrid took the unprecedented step of announcing: "There is no substance in these reports whatsoever."
Ronaldo, himself, has previously insisted that the only team he would play for in England is United.
Becoming a City player while Ferguson is still in charge at Old Trafford would be a massive step for the star to take.