You can make an offer and ask them to counter it. If they won't without more information then you can tell them that is all you will do. Remember that the longer you wait the more interest and fees will be added to your account.
Make sure you understand the ownership of the debt. It is not ussually sold many times it is usually placed by the creditor with multiple different collection agencies.
Also, if the account is currently with a law firm you are in a greater risk of being sued then if it is with the debt buyer or a collection agency.
These are all factors in how you want to negotiate. Depending on the dollar amount, you might want to hire a lawyer to do the negotions for you. Many firms, including mine, give a brief free consultation to determine the situation and if they can help you.
I would add that sometimes the law firms buys the debts. If they buy the debt, this changes the dynamics. They only get paid if you pay them vs. hourly/flat attorney fees.
You can demand they prove they own the note, but they can sell this debt as many times as there is a buyer. But the more transfers, the less likely they can prove the debt.
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If you live in Arizona, please contact me for actual advice; this is just speculation. It certainly is not legal advice. I don't have enough information to give actual legal advice. I can only take the limited information presented and provide a idea of what you might do and how it may turn out.
I'd talk to a decent consumer lawyer in your state: there are many. One thing you'll want to know is what statute of limitations applies. Maybe the debt is too old to be sued. If that is teh case, you have greater leverage. I would not be quick, at this point, to offer more financial information.