Wenger is under increasing pressure at the Emirates following Sunday's 2-1 defeat to Tottenham Hotspur in the North London derby.
The Gunners need a dramatic improvement to secure Champions League qualification, with Chelsea five points ahead in fourth place.
Brady believes that Wenger is the right man to restore Arsenal to their former glory if he is given the resources to make changes in the summer.
He told the Daily Mail: "I hope that Arsene is given the resources to spend and have a go at putting us back where we were eight years ago.
"I think he should be given that chance and, from where I am in the club, I don't think there's any pressure on him, I think the board are 100% behind him.
"When you get beat by your neighbours it can get a lot of people talking, particularly people ringing up radio stations and things like that. But I think we've got to keep it all in perspective."
Brady has been involved in developing young talent for Arsenal since Wenger took over at the club in 1996.