United and Chelsea's hopes of landing the player had been raised following reports in Spain that he has rejected a new contract offer from Bayern Munich.
Bayern have been at pains to emphasise that Ribery is not for sale this summer, putting a prohibitively high price tag on his head to warn off potential bids of around £100 million.
A report in Sport, a Barcelona newspaper, details Bayern's offer to the Frenchman of around £7.5 million a year, as the Bundesliga club look to hold on to one of their most valuable assets.
Ribery himself, however, has expressed a preference for joining Real in an interview with a French newspaper.
"I have decided that I want to leave. It will be Real Madrid or nothing," he said.
"I will wait to see how things pan out but I would like to hold talks with the Bayern management soon."
However, Uli Hoeness, Bayern's general manager, does not believe Ribery's desire to leave alters their position.
"Does Franck want to go to Real? For us, that changes absolutely anything. Life is not always a fairytale," he said.
"Real have not made us a specific proposal and we do not need their money."
After the transfers of Kaka, Cristiano Ronaldo and Karim Benzema – all to Real Madrid – Ribery is the most sought after talent on the continent.
With Ronaldo commanding a fee of £80 million Bayern can realistically expect to do business for somewhere in the region of £55 million should they decide to cash in on the 26-year-old, despite former coach Ottmar Hitzfield suggesting that Bayern would only be interested in an offer in the region of £75m.
Real Madrid had been heavily linked with Ribery earlier in the summer and, despite taking their spending past the £170m with the acquisition of Benzema, show no signs of finishing their shopping spree just as yet.