Tell them that unless they mail a debt validation letter showing you owe this debt to them, then per the FDCPA, you will not pay them. A debt validation letter includes the original creditor, the original loan amount, the amount of money still owed, the loan date, date of last payment made and if the company has the legal right to collect said debt.
It is a violation of the FDCPA (Fair Debt Collection Practices Act) to refuse to mail this documentation to you - in fact, your caller has five days from the date of their first call to you to mail this. Do not accept email or fax. If they continue to call you and refuse to provide this information, try to get their company name, mailing and physical address and report them to the FTC, FCC and your state's Attorney General. Never take anyone's word that you owe them money - per the FDCPA, debt collectors (and lawyers if they're working as debt collectors) must provide proof that you owe them.