The Conservative Party has been reported to be in talks with the commercial television network to secure a primetime slot for Cameron's programme.
Brown's successful appearance on Piers Morgan's Life Stories went a long way in reviving his sagging rating with the voters.
Cameron has apparently turned down an invitation to appear on the same show. Reports says he would prefer a programme such as a documentary to an interview. The Tories want ITV to telecast the programme before the general election.
Cameron recently gave an emotional interview to STV where he spoke about the death of his six-year-old son, Ivan.