First off, the FBI doesn't usually keep a file on past debts unless it is related to a terrorist act.
Regrettably, personal information is often traded, misused, and often misrepresented. If you suspect a scam and are not familiar with the bill that they are trying to collect, file a police report on it. You can also verify the company collecting the bill through a quick search on Google. If they have a website look for a way to contact them, see if it matches the phone number you were given, if not call and ask about the person that called you. They may be able to provide more information on the debt collection to help you determine if it is actually yours. if they have never heard of the person then it will make them aware of the problem. If you are familiar with the bill or it sounds like something you may have had, call the company that this guy is supposedly collecting for and ask about which collection agency they assigned your account to.
If you can not find your answers through any of these routes then it is probably a scam. If he calls again request that he submitted the collection information to you in writing. If he has to ask for your address then he probably is not legit. Tell him that you will resolve the issue once you have received it in writing and only then. Do not volunteer any information. If the guy is legit he will go through the proper channels to ensure that he gets his commission for collecting the debt.