I would have thought he is the "higher-up" - he is the Director of Football and responsible for player recruitment. There will be others involved at different stages, Finance Director, Club Secretary etc... and if you're spending £20M+ the scheme of delegation will no doubt have the CEO as one of the signatories.
I'm like any other fan and constantly hitting refresh hoping another signing has been announced, but this isn't Football Manager or Fantasy football - the people paid the massive salaries they are to negotiate the transfers should be doing their uttermost to get the best deal for the club, if not we'll be known as a soft touch and every player we go in for will have an escalated fee attached.