Falcao has been consistently linked with a switch to Real Madrid in recent weeks, despite only completing a £52m move to Monaco last summer.
Vasilyev has denied claims that Madrid could purchase the Colombian striker at a fixed price agreed in his deal, while insisting that Florentino Perez's declaration of interest was an error of judgement.
He told Marca: "I know Florentino and I have a lot of respect for him. He runs one of the best clubs in the world, but I think some of his comments were inappropriate.
"Falcao has signed a five-year deal with Monaco and I have already said a hundred times that he doesn't have an exit clause.
"We put in a lot of effort in order to sign him and it would not make any sense to allow him to leave again in January or next summer."
The 27-year-old has quickly become integral to Claudio Ranieri's plans in the principality, scoring eight times in 11 matches.