While the Broadcasting Standards Authority is a statutory body funded by the Government, the Press Council and Advertising Standards Authority are industry-funded independent bodies.
The National Government got offside with the Press Council earlier this year when it called for "greater collaboration" among the three organisations.
Arts Culture and Heritage Minister Chris Finlayson was forced to offer an assurance there was no plan to regulate the Press Council or to try to set up a single body to deal with all complaints.
Yesterday, Labour's ICT spokeswoman Clare Curran said the convergence of various forms of media, such as video content on newspapers' websites, meant the existing regulatory models needed to be examined to ensure they were "fit for purpose".
"I don't want to buy a fight with the Press Council because they do perform a really important role, as does the BSA, but the two mediums are merging and if that doesn't set up the need for a discussion what does?"
Press Council chairman Barry Paterson said Labour's proposal sounded similar to that which the Government had backed away from earlier this year. He believed combining the functions of the council and the BSA would prove difficult unless Labour was thinking of statutory regulation of the Press Council.
That would "probably not" be welcomed by the industry," Mr Paterson said.
"I suspect they wouldn't be prepared to fund it on that basis and we would be probably the only country in the world that would have statutory regulation of the press."