|Before trying to get this employee to back off or get off your back, it is important to step back and look carefully at his behavior. If he is truly spending too much time trying to do your job rather than his, then he needs to be given some specific advice as to his own job priorities, responsibilities, and objectives. He needs to understand that you are still open to his ideas and inputs, but his own work comes first.
It also sounds like he is approaching you with an air of arrogance and elitism. If this is actually the case, you should give him some advice as to the way to present his thoughts in a more persuasive and compelling manner. He needs to understand that his style may be preventing the substance from being heard.
If you actively close the door on him, you may be inadvertently sending a message to the rest of the team that you are not receptive to their ideas, and this clearly works against effective management today. And, it plays right into what he has been telling you.
Since he is playing manager right now, he is presumably interested in becoming a real manager at some point in the future. Unless he wants that to be in the very distant future, he should listen to your "suggestions."