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.
And Nice-Matin claims Henry has targeted Koscielny, along with others, as a potential recruit.
Thierry Henry looking to add experience to Monaco defence in January. Laurent Koscielny, Gary Cahill, Pepe and Martin Skrtel all on Monaco radar, according to Nice Matin
— Matt Spiro (@mattspiro) December 19, 2018
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.