Having not featured for the Gunners since November last year, the 32-year-old is now playing with the club's Under-23s side and has been informed by Wenger that he can leave on a free.
Brighton & Hove Albion were reportedly considering taking him in the final days of the transfer window but an offer failed to materialise, while a proposed move to Nice fell through when they decided to sign Christophe Jallet instead.
"I don't know what will happen because this summer the coach would have let me leave without a transfer fee," Debuchy told L'Equipe of his future. "Brighton also enquired in the last few days of the transfer window. But that came to nothing.
"I cannot predict the future. Some clubs are maybe scared that I haven't played for a while. Maybe my salary is also a problem although I am ready to make an effort on that. I am going to give my best and we will see. I am taking the initiative."
"I am training with the professionals during the week and I am playing with the youngsters at the weekend. I am not the future."
Debuchy moved to the Emirates from Newcastle United in a £12m deal three years ago but has since made just 13 top-flight appearances for Wenger's side.