You don't need to. The LAW is sufficient:
http://www.ssa.gov/history/reg1.html
No member, officer, or employee of the Board, except as authorized by this regulation or otherwise expressly authorized by the Board, shall produce or disclose to any person or before any tribunal, directly or indirectly, whether in response to a subpoena or otherwise, any record (including any file, letter, application, claim, return, report, or other paper or document) or any information acquired therefrom or otherwise officially acquired, pertaining to any person.
The law itself prevents the official generation of reports unless consent is given to the Department by the individual in question. Since anyone reporting to the Department does so via the instrument of their SSN, they can't very well give consent for an official report to be generated without it.
An "illegal" person is simply unknown to the department, and if they're unknown then they can't very be included in the statistics can they?
There are known knowns; there are things the Department knows they know. They also know there are known unknowns; that is to say they know there are some things they do not know. But you are asking to provide details of unknown unknowns.