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What if you told them, "If I get this position, I'll be expecting a budget between x and y. Does this seem about right?"

Or how about, "If I get this position, what sort of budget can I expect to be working with and what will I be expected to produce with that budget?"

Yeah, that's better.

What would you base that budget on, without in-depth internal knowledge ?

I was just thinking ballpark, order of magnitude kind of stuff.