ESPN reports that the club, where Henry won the Ligue 1 title in the 1996-97 campaign, have decided to sack Leonardo Jardim.
Jardim will lose his job with Monaco after a dismal start to the season that sees them marooned in 18th place in Ligue 1 nine games into the season, one point off the foot of the table.
Monaco have not won since the opening day in any competition, and Sunday’s loss at home to Rennes extended their run of consecutive defeats to four games, and 10 matches without a win.
Henry, who had been courted by Championship side Aston Villa, is currently assistant to Roberto Martinez with the Belgium national team.
Monaco had also considered Robert Pires, River Plate coach Marcelo Gallardo and former Paris Saint-Germain boss Laurent Blanc.