Vasilyev said the deal for the Colombian, who has scored 28 times in the Primera Division this season, is "on track" but "not yet finalised".
He told RMC: "It is on track, but it is not yet finalised, there are still details to work out.
"We really hope to complete the signing of this great player. He is one of the best players in the world, we will be very happy when he signs."
There have been reports of a clause in the deal which would allow Real Madrid to sign Falcao from Monaco, to avoid him moving to the Bernabeu directly from their city rivals, but Vasilyev rubbished the idea.
"No, if you sign Falcao for one year, that does not do anything," he added. "There is no clause with Real Madrid, I can say that. There is no other choice for building a team."