Since Brady joined the club in 1996 they have not finished outside the top four and have not failed to qualify for the Champions League in 16 seasons.
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 per cent 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.
"The majority of the fans are behind him, the staff are behind him and I think the board are behind him. So we wait to see what the future brings."