Internet rumours surfaced on Monday night, quoting beIN Sports as saying the Colombian striker had agreed to join the Champions League winners.
Doubts swiftly grew about the veracity of the claims, which were conspicuous in their absence from the boardcaster's output.
And beIN Sports officially distanced itself from the story on Tuesday morning, tweeting: "Contrary to certain information, beIN Sports formally denies having announced the transfer of Falcao to Real Madrid."
Nevertheless, Falcao is still thought to be high on Real Madrid's wishlist as they bid to win back the Liga title from city rivals Atletico Madrid.
Falcao left Atletico for Monaco last summer in a £50 million deal, but had his season cut short by a serious knee injury that also ruled him out of the World Cup.
While the Monaco move has been touted by some as a 'bridge' to allow him to switch from one side of Madrid to the other, Eurosport France's Cedric Rouquette remains sceptical, citing Monaco's zero income tax regime as a reason to stay put.
He said: "Falcao has spent time claiming he is ready to stay in Monaco, where he earns wages almost impossible to reach anywhere in Europe without Monaco's tax policy."
- Sports & Recreation
- Real Madrid