The report was leaked to Fairfax reporter Andrea Vance.
Fairfax Media quoted its executive editor Paul Thompson as saying all efforts to attempt to force it to release the emails would be resisted.
"We will resist any attempt to force us to release that sort of information.
"It's the most fundamental commitment we make to our sources. We will go as far as we need to to protect that information."
The privileges committee is a group of MPs which hears cases such as misleading the House. It can summon people, papers and records, which potentially extends to requiring the Parliamentary Service to hand over the emails on its server.
It will be up to the Speaker to decide whether to refer the matter to the committee, which can impose penalties from censure to suspension or expulsion from Parliament.
Mr Dunne resigned as a minister last week after an inquiry by David Henry into the leak could not rule him out and said he refused to provide information, including more than half of the 86 emails between himself and Vance in the lead-up to the leak.
Mr Dunne has continued to deny leaking, but has said some of his actions after receiving an advance copy of the report were enough of a lapse of judgment to warrant his resignation.
He has said those emails would exonerate him, but refused to release them because he believed in the public's right to communicate with MPs in confidence. He said that extended to journalists.
This morning Prime Minister John Key said he had done his job by setting up an inquiry and expecting Mr Dunne to comply.
He told Radio New Zealand that people generally complied with inquiries.
"And if they don't comply, then that of itself often speaks for itself.''
Mr Key said the terms of inquiry did not allow Mr Henry to compel the release of the emails.
"The privileges committee might be able to I think.''
He said an MP would have to lay a privileges complaint before the matter was considered by the Speaker.
Asked what he would do next, Mr Key said: "In the end, the public will judge Mr Dunne.''
He said Mr Dunne had "paid a very high price''.
"He's lost his ministerial warrant, he's being judged in the court of public opinion. And it's for him really to have to reconcile that.''
Winston Peters said he had referred the case to the police and was looking at other possibilities. He had seen "electronic communications of more than one category".
Mr Dunne did not return calls yesterday.
United Future president Robin Gunston said the party still intended to apply to the Electoral Commission to re-register today and had more than the 500 members required. He hoped Mr Dunne would stand in 2014.
- additional reporting APNZ
