The World Cup winner is leaving the coaching staff at the Emirates to focus on his role as television pundit.
Thierry Henry celebrates after scoring
The France and Gunners legend had been taking his coaching badges at his old club while also commentating for Sky Sports and the BBC.
Now Wenger has sought to bring Henry on board on a permanent basis, by asking him to coach the Under 18s.
Arsenal manager Arsene Wenger
But it was an offer with conditions, as the Gunners boss is said to have told his former player that he would have to step away from his media work to focus on his work at Arsenal.
The report goes on to say that Henry has snubbed that offer, as he is eager to maintain his lucrative punditry role with Sky. He will now have to find another club with which to complete his badges, with fellow Gunners legend Tony Adams taking the role offered to Henry.
Arsenal's Thierry Henry celebrates victory
The 38-year-old is the club's record goalscorer, scoring 228 goals in an astonishing eight-year spell, topped off with a short loan at the end of his career.
Wenger has traditionally looked to bring former Arsenal players back to the club as a member of the coaching staff, with ex defender Steve Bould his assistant with the senior team. Robert Pires and Freddie Ljungberg have also taken up roles with the London outfit.
But with the likes of Patrick Vieira, Mikel Arteta and Dennis Bergkamp moving elsewhere to take their first steps into coaching, Gunners fans will be disappointed to hear that Henry is also set to leave the club once more.
Arsenal's Thierry Henry celebrates after scoring