On Thursday, it was confirmed that Falcao, 31, had penned a new three-year contract with the Ligue 1 side, which would run until the summer of 2020.
The former Manchester United and Chelsea striker scored 21 goals in 29 Ligue 1 appearances during the 2016-17 campaign as Monaco landed their first league title since 2000, and Vasilyev has said that the contract is another statement of intent.
"I am very happy that Falcao has extended his contract with the club," Vasilyev told reporters. "I have always said that he is one of the best strikers in world football and this season he has proven that his talent is intact.
"It's satisfying to keep him as a goalscorer and a leader of our team. After this outstanding season, it demonstrates once again our ambition for the future."
Falcao initially joined Monaco from Atletico Madrid in 2013, but scored just 13 times for the Ligue 1 club before moving to Man United on loan in the summer of 2014, and then Chelsea one year later.