Colombia international Falcao has been heavily linked with a number of Europe's top clubs and speculation intensified when he was left out of Monaco's squad for a 1-1 draw with Lille, despite initially being named as a substitute.
Reports of a tweet from Falcao, which apparently read: "Dream come true #HalaMadrid", appeared to suggest a move to Real Madrid could soon become a reality.
However, that message was soon deleted prior to another tweet that sought to clarify matters.
It read: "I have to deny a story about a tweet that I have not done and that is a photo mount."
The former Atletico Madrid striker has scored 14 goals in 24 appearances for Monaco, having missed the latter part of last season and the World Cup due to a cruciate knee ligament injury.
Should he complete a move back to Spain, he would form part of a star-studded Real frontline, which already includes former Monaco team-mate James Rodriguez as well as Cristiano Ronaldo, Karim Benzema and Gareth Bale.