Jardim was sacked on Thursday, with Monaco currently 18th in Ligue 1, having taken one win from their opening nine games.
Henry has been heavily linked with the post as he looks for his first managerial job, having held talks with Aston Villa before the appointment of Dean Smith as their new manager.
Monaco have yet to comment on the reports around Henry's apparently imminent appointment, but Henrichs admits that he would love to work under the former Barcelona, Arsenal and New York Red Bulls striker.
"For me, he's an extraordinary player, a legend of Arsenal," he told L'Equipe.
"It would be interesting if he comes here. But I can't say more."
But Monaco's talented young squad has been decimated by sales since then, with stars including Kylian Mbappe, Bernardo Silva, Thomas Lemar, Fabinho and Benjamin Mendy all departing.
Monaco were beaten 2-1 at home by Rennes in their last match to seal Jardim's fate, with an away fixture against Strasbourg next up as they look to get back on track, potentially with Henry in charge.