While Wenger will not stop Brady from helping out the Ireland team, he has stated that any new job that the former Gunners player does take up must not clash with his current role at the club.
He is very important to us because he is in charge of the youth set-up here," Wenger told the club's official website.
"It wouldn't be a problem if it doesn't stop him doing the job he does here properly. I haven't spoken to him yet as he was away but I will when he comes back.
"I am not against it as long as it is not too demanding time-wise.
"At the moment I cannot come out and talk about it because I don't know how long this new job will take."