The Ligue 1 club approached the current Belgium assistant gaffer to replace Leonardo Jardim who was axed on Thursday.
Talks between Monaco and Henry, 41, are at an advanced stage and terms will be finalised when Arsenal's record scorer jets into the country tomorrow.
Monaco sacked Jardim, 44, with the club 18th in the league and just one win on the board this season.
They won Ligue 1 in 2017 but went on to sell almost half a billion pounds worth of star players in Kylian Mbappe, Bernardo Silva, Ben Mendy, Tiemoue Bakayoko, Thomas Lemar and Fabinho.
Henry would be tasked with first ensuring his former side are not relegated, while their aim is to return to the top of the table.
The Frenchman was appointed Belgium's assistant manager under Roberto Martinez in 2016 and helped steer them to third place at this summer's World Cup.
Henry was heavily linked with the Aston Villa job before the club appointed Dean Smith.
Arsene Wenger, who signed Henry for Arsenal, endorsed his former player to become Bordeaux boss when he was linked with the job in August.
He said: "He is intelligent and he has the qualities."
Jardim, who leaves Monaco after four years, said: "I am grateful and proud to have been able to coach AS Monaco for more than four years.
"I have always given the best of myself and worked with passion. We have won great victories together and I will always keep those memories in me."
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