Jardim was linked with the Arsenal post before Unai Emery arrived at the Emirates Stadium, while Chelsea have also previously been credited with an interest in the 43-year-old.
Vasilyev, however, has said that Jardim is "ideal" for Monaco, and has hinted that the Portuguese will remain in charge of the principality outfit entering the 2018-19 campaign.
"At the time he arrived, it was complicated, and I had met several candidates," Vasilyev told Goal.com. "He had results behind him, it's true, but when I spoke with him I felt his personality and his intelligence. I said: 'OK, he's the candidate.'
"I am happy that life has proved me right because I was behind his arrival in Monaco. He is ideal because he fits into this project. Indeed, it became his project."