Henry is currently mulling over what do to next after playing his final match for New York Red Bulls last weekend.
At 37, the iconic French striker is approaching the end of his illustrious career and has spoken of his desire to return to Arsenal in some capacity when he does hang up his boots.
Current Arsenal boss Arsene Wenger is convinced that the club's record scorer is destined to go back to the north London team. And Parlour thinks that Henry will be Arsenal boss at some point if he has an interest in taking charge at the Emirates Stadium.
"I think he will definitely get involved with Arsenal," Parlour told talkSPORT.
"I certainly believe, one day, if he really wants to be a manager, he will be manager of Arsenal.
"He was such an intelligent player. Arsene Wenger used to have a meeting on a Monday with the players after a game and Thierry would always have his say.
"He would make some great points, not just about forwards, but about defending and how we defend as a team.
"He always had that charisma to be a manager. And look at his name around the world. People would want to play for him and he would attract big players."
