Jardim, who has endured a torrid start to the 2018/2019 season has lost five of his opening nine games of the season, leaving the club at a lowly 18th in the table.
"I am grateful and proud to have been able to coach AS Monaco for more than four years".
With one a more elder figure and one younger, they are a better balanced duo than Henry and Terry might have been together, and they have worked together before.
"I want to express my profound respect for all the work Leonardo has done", Vasilyev said.
The club from the principality would not comment on a replacement, but their former player Thierry Henry has been linked to the job.
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Jardim led the club to another French title in 2017, their first since 2000. Leonardo established himself as a reference point in Europe and left a very positive balance.
"His time here will remain one of the most handsome periods in the club's history. Leonardo will always be part of the family of AS Monaco".
Henry, who is now working as Belgium assistant manager alongside boss Roberto Martinez, is the favourite to replace Jardim, whose Monaco side are 18th in the Ligue 1 standings with only one league win from nine games.
He is still Roberto Martinez's assistant for the Belgium national team, but is said to be in negotiations with his potential new employees, with the report suggesting that only a few details need to be ironed out.
According to Sky sources, the Villa hierarchy are no longer interested in hiring Henry after the sacking of Steve Bruce earlier in the season.
Henry was reportedly set to take his first step in management at Ligue 1 club Bordeaux this summer, but that never materialised.