The 44-year-old coach, who was crowned Ligue 1 Manager of the Year in 2016/17, will likely be replaced by former Arsenal and FC Barcelona striker Henry.
The Ligue 1 side announced Jardim's departure from the club on Thursday after dropping to 18th on the log, having won only one league game so far this season.
However, the club have made a poor start to the new season, failing to win any of their last 10 games since the opening day of the league campaign including losing each of their last four outings.
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.
Speaking to the club's official website, Jardim said: "I'm grateful and proud to have been AS Monaco coach for more than four years. We achieved some great victories together and I'll always keep those memories", his statement read in part.
"Leonardo established himself as a reference point in Europe and left a very positive balance", said Monaco vice-present Vadim Vasilyev.
Aston Villa have received a setback in their managerial search with Thierry Henry reportedly snubbing them in favour of Monaco.
"His time here will remain one of the most attractive periods in the club's history".
Jardim took over at Monaco in 2014 and counts the likes of Sporting CP, Olympiacos and Braga among his former clubs.
Rumours are rife that Monaco are on the cusp of sacking their manager Leonardo Jardim following a wretched start to the new season.