If they ask for a reason, tell them you are not ready to discuss it right now. Then get off the phone. Period. Do not discuss why you are not ready to discuss it. The more you are pressed to rent the greater liklihood the applicant is not qualified. If he was such a great applicant he would move on to other listings.
Not to mention that there are things that can slow down the application process. For example leaving an item blank on the application. Or trouble verifying information. Take Jake's advice but also realize that there are other reasons to not take him if you get in a corner. Chances are if he is pushy and demanding there is a reason for it. You will likely find troubles on the app. that would not make you ready to accept him without further due diligence.
Continue to market and show the property and worrying about this person is a sideline to your true goal.