Claims that three senior newspaper executives misled Parliament over phone hacking are set to be referred to a watchdog with the power to recommend sanctions.
MPs will decide whether to pass the allegations to the Commons standards and privileges committee after debating the conclusions of a cross-party investigation.
Ex-News of the World editor Colin Myler, the paper's former legal manager Tom Crone and one-time News International chairman Les Hinton all deny giving misleading testimony.
The accusation was among the highly-critical conclusions of a lengthy inquiry into the hacking scandal by the influential culture, media and sport select committee.
Although the committee was split in its final report over the most strident criticism of Rupert Murdoch, it was united in stating that his media empire had misled the inquiry in a "blatant fashion" and in the accusations against the trio.
Speaker John Bercow opened the door to the complaint being escalated yesterday when he granted the committee's chairman, Tory MP John Whittingdale, permission to table a motion.
"Having considered the issue I have decided that this is a matter to which I should allow the precedence accorded to matters of privilege," he said in a short statement.
Mr Whittingdale's motion, which could trigger a vote, calls for the conclusions of his report to be referred by MPs to the standards and privileges committee, which is made up of MPs.
If passed, the committee will produce its own report and make recommendations about what punishment, if any, the former News International executives should face.
The power to punish non-members of the Commons is so rarely used it is unclear what sanctions would be open to MPs.
But the men could be summoned to the bar of the Commons for a public dressing down.
The Government last month launched a consultation on parliamentary privilege in an attempt to clarify the situation.
It noted that the Commons' power to issue fines was last used in 1666 and may have lapsed and that no non-MP had been punished by the House since a 1978 agreement to use penal powers sparingly.
The last member of the public to be summoned to the bar of the House of Commons was Sunday Express editor John Junor who appeared before MPs in January 1957.
The newspaper had published a piece criticising petrol allowances given to political parties in constituencies.
He was rebuked by MPs for failing to "establish the truth of the article" and not being willing to "admit its obvious implications". He apologised and no further action was taken.
The last fine imposed on an offender by the House was on February 6, 1666 when Thomas White was ordered to pay £1,000.
White absconded after being ordered into the custody of the Serjeant at Arms, for causing Henry Chowne, the MP for Horsham, to be arrested and prevented from attending Parliament.
The last imprisonment by the Commons of a non-member was of Charles Grissell in 1880 for a breach of privilege in connection with the committee on the Tower High Level Bridge (Metropolis) Bill.
In 2010 a leading law firm was found to be in contempt of the Commons after threatening an MP with legal proceedings if he made allegations about one of its clients in the House.
The Standards and Privileges Committee criticised Withers LLP for failing to realise that John Hemming, a Liberal Democrat backbencher, was protected by parliamentary privilege.
But it made no recommendation for further action after receiving an apology.
Mr Whittingdale said misleading Parliament was regarded as "a very serious matter.
"If a committee decides it has been misled, then clearly there has to be some further action that follows from that.
"The fact the Speaker was willing to grant the debate as a matter of priority is an indication that he too regards this as very serious," he said.
He said the motion would also relate to wider corporate responsibility.
Mr Hinton, Mr Myler and Mr Crone have all denied misleading the committee.
Mr Hinton described the committee's conclusions as "unfounded, unfair and erroneous", while Mr Myler said he stood by his evidence to the committee.
Mr Crone said he did "not accept" the allegations, adding that he seems "to be the subject of serious allegations which lack foundation".
The debate comes as Labour committee member Tom Watson - prominent among those who sought to expose the extent of phone hacking - gives evidence to the Leveson Inquiry on media ethics.
Mr Watson tabled the amendment questioning Rupert Murdoch's fitness to run any company that split the committee and has been a vocal critic of News International.
Also appearing today are Labour former cabinet ministers Lord (Chris) Smith, who was culture secretary during the first term of Tony Blair's government, and Alan Johnson.