The Colombian striker joined the French outfit for a mouthwatering £51 million this summer and reports last month had insisted that the striker was already unhappy at the club - leaving the likes of Chelsea and Manchester City interested.
And in recent weeks, Falcao has been linked with a move back to Spain, with Real Madrid potential suitors.
However, with a trip to title rivals PSG on the horizon, Vasilyev has insisted that the club's prize asset will not be leaving the club.
And speaking to L’Equipe, Vasilyev stated: "There’s no clause in his contract that might allow him to leave after a year.
"It wouldn’t make any sense to build a project around a player who could leave us after one season.
"There are always people who have an interest in these rumours… I would just remind you that negotiations between Tottenham and Real Madrid [for the transfer of Gareth Bale] were very difficult."
Monaco have started strongly in Ligue 1 this season, winning four and drawing one of their five league games, however they will face their toughest challenge yet when the play the champions PSG this weekend.