The Arsenal legend is winless after five games in charge and suffered his third defeat in a 4-0 loss to Club Brugge.
Ladbrokes also have the Frenchman at 5/2 to return to Sky Sports as a pundit within the next six months.
The 41-year-old has struggled to stop the rot at the Stade Louis II as they remain bottom of Group A in Europe and have slipped to second bottom in Ligue 1.
Monaco are yet to win in their last 15 matches in all competitions, which began while Leonardo Jardim was in charge.
This is Henry's first role as manager, after working as Roberto Martinez's assistant for Belgium at the World Cup.
Alex Apati of Ladbrokes said: "Henry may well surpass Gary Neville as Sky Sports' most unsuccessful pundit-turned-manager but if the latest odds are anything to go by, there's probably a seat waiting for him back in the studios."
Neville was sacked by Valencia less than just four months after he employed as manager of the Spanish side.
The Manchester United legend won just three of their 16 La Liga games and 10 of 28 games overall – which included a 7-0 defeat to Barcelona.
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