Talks are expected to take place between every top-flight club next month about whether to change the deadline of the current window so that it shuts before the first game of the new season.
At least 14 of the Premier League's 20 clubs must agree for a new rule to be introduced, and Brady is confident that support for an early window closure is widely supported among the top tier.
"We'd started debating this around March 2017 at the Premier League and 17 clubs were broadly in favour of the window being closed," she told Sky Sports News.
"I think the main issue is that it protects the integrity of the squad, you know where you are, you have to get on with it and the players know that.
"It's mainly for the club, fans and manager to know - this is who we've got, this is the squad, these are the numbers, on we go. I think to close the window early, for the integrity of the league, is the right decision."
Clubs from other European leagues would still be allowed to sign players from England in line with their own domestic deadlines.