He also investigated last election's Teapot Tapes.
The information hacked from Slater's computer formed the backbone of Nicky Hager's book Dirty Politics, which painted a picture of a National government which used right wing blogs to carry out attack politics.
Police minister Anne Tolley said she was not aware of a complaint from Slater.
"I can't get involved in police operations or how they deal with complaints, and I would expect any claim of illegal activity on any matter to be properly looked at."
Despite some media reports, Mr Burgess is not "investigating" any complaints.
Police have so far received two complaints. Those include one from Mr Slater and another from a political party.
The complaints are being coordinated through the Office of the Assistant Commissioner Investigations at PNHQ, which is acting as a central point to collect any complaints, before being assigned to the appropriate staff for follow up.
Police will be making no further comment while these matters are being assessed.
How long the process may take is unknown.
Watch: Hager book: 'Key has a lot to answer for'