And they are prepared to offer £65million plus a player to land the superstar, 28, who is still a hero with the United faithful.
Ronaldo is also understood to be keen on the move.
He has turned down offers from Real Madrid to sign a new deal with only two years left on his current contract.
Real will not give up trying to keep him.
But they have already made contingency plans to bring in Gareth Bale from Tottenham in a switch worth £80m.
They also know that they cannot afford to let Ronaldo’s contract run down and now would be the last chance to get big money back on him.
Ronaldo has put his house up for sale in Madrid and did not play in Real’s final game of the season after falling out with departing manager Jose Mourinho.
The player left United for Madrid in an £80m move in 2009. While he has won a Spanish title and the Copa Del Rey, he has not always been happy at the Bernabeu.
He missed many of his old team-mates at United and kept in touch with Alex Ferguson.
Ronaldo was disappointed when Fergie retired but he still fancies a return.
United have made contact with his representatives.
Sponsor Nike are also in on the deal.
United would make him their joint top earner with Wayne Rooney on £250,000 a week. While Paris Saint-Germain could top that, it is not just about the money for Ronaldo.
The signing would give David Moyes the perfect launchpad for his Old Trafford reign.(www.thesun.co.uk)
