The 31-year-old netted 30 goals in 43 appearances in all competitions this term and Monaco are keen to prolong his stay at the Stade Louis II, with his existing deal due to expire in 2018.
"I can confirm that we will offer Falcao a contract renewal," Vasilyev told Telefoot.
Head coach Leonardo Jardim played a major role in Falcao's resurgence and Monaco are keen to hold on to the Portuguese boss after he guided Monaco to the French title and the semi-finals of the Champions League.
"We will also have talks with Jardim in the upcoming days, we will try to extend his contract," Vasilyev added.
"I would like him to stay at Monaco a long time.
"Jardim is our coach and so long as he has not said that he wants to leave, he will remain our coach."
Jardim has been in charge of Monaco since 2014.