Ronaldo's future at United has been the subject of constant speculation, with Real having trailed his signature for the last three summers.
Real president Florentino Perez has made no secret of the fact that he would like to lure Ronaldo to El Santiago Bernabeu.
The Spanish titans have now agreed an £80million offer for the Portuguese ace and United have given the World Player of the Year permission to talk to the capital club.
Ronaldo will head to the Spanish capital to hold discussions with Real and undergo a medical.
Real have already snapped up Brazilian superstar Kaka in a world-record deal, but a move for Ronaldo would significantly eclipse that figure.
"Manchester United have received a world-record, unconditional offer of £80million for Cristiano Ronaldo from Real Madrid," read a club statement.
"At Cristiano's request - who has again expressed his desire to leave - and after discussion with the player's representatives, United have agreed to give Real Madrid permission to talk to the player.
"Matters are expected to be concluded by 30th June. The club will not comment until further notice."
Real confirmed the news in a brief statement on their website, adding that they hoped to finalise matters as soon as possible.
"Real Madrid confirm they have made an offer to Manchester United for the acquisition of the rights of the player Cristiano Ronaldo. The club hope to reach an agreement with the player in the next few days."
The news is bound to be greeted with some scepticism by United fans, who have repeatedly been told no deal had been agreed for the sale of FIFA's World Player of the Year in the face of regular statements from Spain the former Sporting Lisbon star was bound for the Bernabeu.
It was even suggested Ronaldo would be due a £20million compensation fee from Real if the deal did not go through by June 30, the date United now state themselves as when they expect matters to be concluded.
It now remains to be seen where the transfer fee could be reinvested in a squad that almost, but not quite, proved good enough to win back-to-back Champions League trophies, in addition to a hat-trick of Premier League titles.
The name of Bayern Munich's Franck Ribery is bound to crop up as a potential replacement, although the 27-year-old seems overpriced at the £40million figure being bandied about in some quarters, with Wigan's Antonio Valencia also in the frame.
Ferguson will certainly be making plans already to ensure his new faces are on board before United head to Asia for their pre-season tour.
Amid the frenzy over Ronaldo's impending departure, it is bound to be asked whether the current debt hanging over United of almost £700million has played any part in the decision to accept Real's huge bid.
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Man Utd should spend that on a couple of good players like David Villa and Frank Ribery
.....SELLING YOUR BEST PLAYER IS A SIGN OF WEAKNESS (no money in da bank!)