The former Arsenal striker took charge of Monaco in October but finds his side languishing in 19th place in the Ligue 1 following a poor start to the season.
Top players such as Kylian Mbappe, Thomas Lemar and Fabinho’s departures from the club over the summer haven’t helped Monaco or Henry’s cause.
But with the January transfer window only weeks away from opening, Henry will be looking to improve and reinforce his squad.
And Nice-Matin claims Henry has targeted Koscielny, along with others, as a potential recruit.
Koscielny, 33, has made just three appearances for the Gunners this season having returned from his long-term Achilles injury earlier in the month, but Henry will be hoping that he can convince his former teammate in joining him at Monaco.
However, Unai Emery may be reluctant to sell the Frenchman next month following a lack of defensive options at his disposal due to injuries.