Falcao joined United on loan with a view to a full transfer in September of last year. But the Colombia international has been unable to live up to expectations at Old Trafford, scoring just four goals in 25 appearances for Louis van Gaal's men.
United have the option to sign the former Atletico Madrid man for £43.5 million at the end of the campaign.
And, despite his disappointing season, Vasilyev told Nice-Matin: "I saw the Manchester United people last Sunday and they have not yet decided if they would exercise the option.
"It’s not his best season, but they kept the opportunity to make a decision at the end of the season.
"We are not in any other negotiations, even if big clubs are interested. The decision is with Manchester, then we will discuss with the player what he wants. I would like to have more visibility."
Explaining the reasons for Falcao's departure from Monaco, Vasilyev added: "He had mishaps in Monaco. He had problems with the coach [Claudio Ranieri], there was a lack of understanding; he was also seriously injured and missed the World Cup.
"In late August, he came to tell us that he wanted to play at a higher level."
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