The papers say that 15 members of the security service have already provided samples.
There was one source of unidentified DNA found in Mr Williams flat.
Police investigating the death of MI6 code-breaker Gareth Williams are to intensify their inquiries into his colleagues and work.
Whatever the coroner's verdict today at the inquest into the death of MI6 spy Gareth Williams, many questions will remain unanswered.
MI6 codebreaker Gareth Williams was probably killed unlawfully but the case might never be solved, a coroner has concluded.