The Gunners captain, and most influential player of all time, is currently on holiday in the United States. The Arsenal squad are scheduled to return for pre-season training in three weeks time, and by then Wenger is expected to know whether or not his plans will again include Henry.
Wenger has had to deal with constant rumours over the future of Henry ever since Arsenal's season was effectively ended by their exit from the Champions League, which also was the final match of an injury-blighted campaign for his captain.
The Gunners boss, however, indicated his relationship with Henry was such that he would be the first to know should the French striker be ready to move on.
"I know the day Thierry Henry wants to leave he will knock at my door and say: 'Listen, I want to go somewhere.' He did not do that," said Wenger at the time.
"Thierry has had a bad season, he would be the first to admit that.
"Still, if you look at the number of games he has played and the number of goals he has scored, it is not as bad as everyone thinks because he has scored 10 [Premiership] goals in 17 played.
"But Thierry Henry was playing 50 games every year, for eight years on the trot.
"In fairness, that is exceptional.
"You know that, one year, he will not be capable of playing 50 games.
"It was after the World Cup final, and the Champions League final. It was certainly too much for him."
Wenger added: "Overall, I feel he is frustrated - but he wants to bounce back next year and have an outstanding season."