The way I think it should work, at Arsenal at least, is that the manager is in full control of the football side of it. By that I mean that you hire a manager who you trust when it comes to the players he wants for his team building and vision on the pitch to work. The manager should early come in with a numbered list of players he wants for every position ahead of the new season, and that is it. That is where his influence should stop.
The suits along with the owner should then handle the rest. Determine how much they are willing to spend, start as high up as possible on the manager's list and open negotiations with clubs and agents/players. The manager should have no input in that part of the operation IMO, and the suits should try to close deals as fast as possible. If the manager is needed to convince a player to sign he should be of course, because that is to do with the footballing side of things.