The French side has insisted that the star attacker is going nowhere amid rumors linking him with the Liga giant.
The Colombia international, who recently returned to the pitch after a lengthy spell on the sidelines due to a knee injury, is continually being linked with a move to the Champions League holder, but Monaco has made it clear the striker is not going anywhere this summer.
MORE: Biggest summer transfers | Soccer's beautiful fans | WAGs
"We have met several times with Real Madrid representatives [during talks for James Rodriguez's transfer], but we never even spoke about Falcao," Vasilyev told L'Equipe. "There has not been an offer and we are not in negotiations. The truth is that Falcao will play with Monaco again in 2014-15.
"Falcao looks happy. I think he's glad to be over the injury and be back with his teammates. Sunday's performance against Arsenal confirmed Falcao's status as a great forward. He missed the World Cup through injury and that's always tough psychologically, but he has character and I hope this will be his season at Monaco."
The 28-year-old, who joined Monaco from Atletico Madrid last year, has a contract with the Stade Louis II side until June 2018.