Should I quote for job

OK, this sounds kind of weird but a have a potential client that wants me to give them a quote to do a quote. They want to pay me for a design of a large WAN/LAN project design. Is it me or does this sound odd.

I lke the idea of them paying me to say yes I will give them a quote. But it is bothering me that they want to know how much it would cost to put it in writing.

Should I make it worth my while to get paid for the design or just do the design for free and hope I get the job of doing the work.

What should I charge or should I charge?

Scope of job is to design the network of a development of high-end apartments (864 apartments in 36 building) using gigibit fiber between building and cat5 to each apartment.