Director Peter Lind said the council had not had detailed discussions about the proposal so far but "if they were looking to put a fee on it we would be very keen to talk to them about it".
The Herald understands vetting is now the only one of a number of areas of activity where police wanted to introduce "cost recovery" or user pays that is still under consideration by the Government.
Police had been seeking a legislative change that would allow them to charge for policing at privately run concerts, wine festivals or sports events but were knocked back.
Police Association president Greg O'Connor said the police were facing huge funding shortfalls over the next few years, "and so if Government are going to insist on police saving more and more out of the budget then the least they can do is give them the ability to actually recover some".
User-pays coming on police vetting
* Vetting aims to protect vulnerable members of society including children, the elderly and those with special needs from risks posed by people with a history of detrimental behaviour.
* Police performed 476,000 checks in the 2010-2011 year.
* The check may result in information being released about criminal convictions, family violence reports and behaviour of a violent or sexual nature that may not have resulted in a conviction.