@Michael G. First off, I'm 100% with @Alex S. and @Thomas S., they can't (currently or otherwise) afford your rental so you need to stop wasting your time with them and move on, find someone who can afford it. My guess would be that even if they do manage to come up with the money initially, you'll eventually have a tenant who isn't paying rent on your hands, and who wants to deal with that hassle, especially when there are plenty of people out there with enough money, etc. to currently afford it. How long has it been on the market? Are you considering this person because you're having issues finding other renters interested?
Aside from that, have you checked to see if they meet your other requirements (income, credit score, etc.)?
Finally, lets address the deposit. First off, this is in no way/shape/form legal advice it is merely my opinion. But fairly confident that you CANNOT call it a deposit and have it not be refundable. My guess would be you'd have to write up something calling it a holding fee that you would retain upon non-performance (i.e. not signing a lease) and that upon performance it would convert into their deposit. Again, not a lawyer but that would be my best guess.
Overall, just pass on them and move on to the next prospective tenant, anything else is too much work/risk.