​Renting to someone who has previously been evicted?

[Michael W.]

Someone is interested in renting a space in a strip center I manage. I had him fill out an application and proceeded to screen him. Not good. He is evasive and failed to provide all of the info asked for, such as landlord referrals and SSN. I learn from a former landlord that he was evicted from a previous address. He currently leases a store at another location and the owners only agreed to accept his tenancy after he agreed to doubling the security deposit and paying a rent premium, with steep escalations in the lease. They say he has kept up with the rent thus far.

He really wants to rent my unit and has offered to pay four months in advance, with subsequent quarterly payments made in advance.

Is this a definite no, or would it be worth signing with someone like this if the terms are attractive?