Leonardo Jardim was sacked on Thursday with the club 18th in Ligue 1, having won just one of their opening nine matches.
Jardim took over at Monaco in 2014 and guided them to their first league title in 17 years in 2016/17, during which Kylian Mbappe was the breakout star for the side.
The defender, who plays for French champions Paris Saint-Germain, is aware that at some point Arsenal legend Henry will leave to follow his managerial ambitions.
"I am grateful and proud to have been able to manage Monaco for over four years", Jardim said.
"There will always be a time when he is going to have to find his way, so we're expecting a break-up, but I hope he stays a little longer with us". "We have won great victories together and I will always keep those memories in me", Jardim told the club's official website.
Vadim Vasilyev, Monaco's general manager, thanked Jardim for transforming the club into a well-respect European outfit.
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"Leonardo has established himself on the bench of AS Monaco as a reference in Europe and leaves behind a very positive balance sheet".
"His time here will remain one of the most handsome periods in the club's history".
"Leonardo will still be part of the AS Monaco family".
Jardim, who led Monaco to the Ligue 1 title a year ago, is reportedly set to leave the club during the worldwide break, with Aston Villa-linked Thierry Henry believed to be in talks with the 18th-placed side.
Henry, who had been courted by Championship side Aston Villa, is now assistant to Roberto Martinez with the Belgium national team.
Martinez has backed Henry to succeed at Monaco, and said: "Thierry is ready to take a club".
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