The Sun says 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 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.