The Monaco striker, who missed Colombia's World Cup campaign because of injury, has been linked with a move to the Bernabeu all summer.
Earlier this week, Monaco coach Leonardo Jardim could offer no assurances on the 28-year-old's future, claiming that he is still a Monaco player "for now".
"For now, he is a Monaco player and I am counting on him," Jardim told French newspaper L'Equipe.
Falcao only joined the Ligue 1 side last season for £50m from Real's neighbours Atletico Madrid, but is reportedly unsettled in France.
It would not be the first time this summer that who you followed on social networking sites played a part in a major transfer. Early last month, Alexis Sanchez's agent began following Arsenal on Twitter, then a couple of weeks later the player joined the north London side.