It appears that an agreement was reached in a meeting on Thursday between Monaco's vice president, Vadim Vasilyev, Nicolas Holveck (general director), Leonardo Jardim and his agent Jorge Mendes.
Jardim was axed in October to make way for Henry.
While Monaco suffered a similar poor run, winning just two of 12 league games since Henry was appointed.
Henry lost his temper in a 5-1 home loss to Strasbourg earlier in the month, confronting defender Kenny Lala in an exchange picked up by television cameras.
Henry recently persuaded former Arsenal teammate and Spain midfielder Cesc Fabregas to join him and help the club avoid relegation.
However, the World Cup victor - who made more than 100 appearances for Monaco at the start of his playing career - has endured a disastrous time in his first managerial role. The Spaniard was given no indication during talks with the club that Henry's future was under immediate threat.
The upheaval at Monaco could also eventually extend to Michael Emenalo leaving his role as the club's sporting director. Henry walked into a veritable mess when he took the job, and his clashes with opponents and hard-line treatment of first-choice players haven't been well-received.
Despite the initial excitement at his arrival, his relationship with several players in the dressing room is understood to have deteriorated and some first-team players were sent to train with the reserve team as the coach doubted their commitment.
Monaco are placed 19th on table, one point off the bottom and their season have encountered one problem to another with Henry unable to handle the situation.
"We must react at Dijon [on Saturday]", he said. I arrived, the club was in a state.
"Asked who would be left out, he replied: "You will see". "At some stage you need lads who want to save the club, who are not just thinking of themselves". Franck Passi took training on Thursday.
Jardim, sacked by Monaco despite leading the club to the Ligue 1 title in 2016-17, has been linked with a return to the club.
"It is absolutely necessary to get something in Dijon this weekend".
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