It is understood that the transfer fee would be made available for Ferguson to invest in the transfer market.
United have been linked with the likes of Lyon forward Karim Benzema, Bayern Munich winger Franck Ribery and Wigan's Antonio Valencia.
Madrid signed Brazilian Kaka for a reported £56m earlier in the week, surpassing the previous world record fee in pounds sterling of £45.6m, which Real paid for Zinedine Zidane in 2001.
Madrid hope for quick Ronaldo deal
That deal was sealed by the ambition of returning Real president Florentino Perez, who previously led the Spanish club from 2000 to 2006 - during the famous galacticos era.
He recently appointed Villarreal boss Manuel Pellegrini as Real's new coach, and had previously made it clear he would do "everything possible" to sign Ronaldo.
Madrid have also been linked with Liverpool's Xabi Alonso, Valencia's David Villa and Bayern Munich's Franck Ribery since Perez's unopposed election signalled the return of their vast spending.
There had been reports that Madrid would have to pay a £26m penalty clause to Ronaldo as a consequence of an alleged "pre-contract" arrangement that had been agreed with the player's representative Jorge Mendes, if the Spanish club did not sign him this summer.
"This was one that was never ever going to go away," said BBC Radio 5 Live chief football correspondent Mike Ingham.
"After the Champions League final he criticised Sir Alex Ferguson's tactics, he threw his toys out of the pram in the derby with Manchester City after he was substituted. He's been very high maintenance. And £80m is hard to resist.
"Personally, I'm very sorry to see him leave but it's absolutely inevitable. If it hadn't been this summer it would have been next summer.
"This could mean they might be able to keep Carlos Tevez, maybe Wayne Rooney can be liberated."
Archive from April: Ronaldo wanting to stay
Tevez's loan agreement with United has expired and the Argentine will cost United in the region of £25m, while Rooney may have more opportunities to play in his favoured central position if Ronaldo leaves.
Ronaldo, who is currently believed to be on holiday in Los Angeles, joined United in 2003 from Sporting Lisbon for £12.2m, but was strongly linked with a move to the Spanish capital in the summer of 2008.
United lodged a complaint with world governing body Fifa last June over what they believed was a deliberate attempt by Real to unsettle the winger.
After a long, drawn-out saga that ran through the summer months, the Portugal international insisted he was happy at Old Trafford and remained at United for the 2008-2009 season.
WORLD PRESS REACTION
Spain's Marca: "The signing of the century."
Spain's AS: "Praise is mixed with criticism for the price, a new world record."
Spain's El Mundo: "Madrid pay for Ronaldo 57 times his weight in gold."
Spain's El Pais: "Florentino Perez lives in another galaxy."
Portugal's Record: "Real Madrid spend 94m euros for Ronaldo in times of crisis."
Italy's Gazzetta dello Sport: "That's not fair. Mad Real. After Kaka, Real Madrid sign Cristiano Ronaldo."
France's L'Equipe: ""Benzema's turn?"
America's Los Angeles Times: "The hair-gel industry in north-west England suffered a catastrophic blow on Thursday."
"Now I understand I made the best decision," Ronaldo told Spanish sports paper Marca after he had made that choice. "I am with Manchester in body and soul."
But the speculation soured relations between the clubs and last December United manager Ferguson said he would not "sell that mob a virus".
And despite Ronaldo's claim that he wanted to remain at Old Trafford, he was the subject of constant speculation during the 2008-2009 season and often gave mixed messages about his future.
If Ronaldo does sign for Madrid, his last appearance for United will have been in the Champions League final in Rome - in which the Premier League champions were beaten 2-0 by Barcelona.
"History will remember him very well in terms of his contribution as a footballer, he'll also be seen as petulant, egotistical and stubborn but he's been a wonderful player," said United We Stand fanzine editor Andy Mitten.
It took time for Ronaldo to find his best form after arriving in England but he became a pivotal player for United, who have won the last three Premier League titles.
In the 2007-08 season he scored 42 goals, which topped the previous club record for a midfielder held by George Best, and was on the scoresheet as United defeated Chelsea in the Champions League final.
His form through 2008 saw him named Fifa World Player of the Year in January, just a month after he won the Ballon d'Or as the European Player of the Year.
Ronaldo was the top scorer for his club last season, with 26 goals, taking his total for United to 118 in 292 appearances.
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