The Liberal Democrats are expected to abstain the vote, despite many of their MPs siding with Labour's call for Number 10 to more closely examine Hunt's conduct, following a string of revelations.
Lib Dem leader Nick Clegg is understood to have told his MPs to "stay away" from the vote, but many are thought to be angry at how quickly David Cameron has jumped to Hunt's defence.
As soon as Hunt had finished a bruising session giving evidence at the Leveson Inquiry into media ethics, the prime minister said that there would be no investigation into whether he may have breached the ministerial code.
Labour MPs are calling for Number 10's adviser on ministers' interests, Sir Alex Allan, to look at whether Hunt failed to give "accurate and truthful" information to Parliament over his contact with News Corp during the £8bn bid process.
Hunt has also been accused of failing to "take responsibility" for the conduct of Adam Smith, his special adviser who quit after it was revealed that he had extensive email, calls and text dialogue with a News Corp lobbyist.
The BBC's sources say that Clegg has privately urged Cameron on several occasions to refer Hunt for an independent review, including before the culture secretary appeared at the Leveson.
Sources say that relations between Cameron and Clegg are "terse" and "bumpy" on the issue, but there is not thought to be a serious rift developing in the coalition.
One source told the BBC that Cameron had at one stage told Clegg that "nobody's interested" in the Leveson Inquiry.
Even if all 57 Lib Dem MPs withhold their support for Hunt by abstaining, it is still expected that the vote will go the government's way.
Some Lib Dem MPs are understood to have wanted to vote with Labour on the issue, but Clegg is concerned that this would put them in an untenable position with their Tory coalition partners.
Don Foster, the Lib Dem culture spokesman, insisted that there were clear reasons why his colleagues should not support Hunt.
"Nick Clegg was absolutely clear from the outset that if, after Jeremy Hunt's appearance at Leveson, questions still remain, they need to be properly addressed," he told the BBC.
"He wasn't consulted by the prime minister on his decision not to refer Jeremy Hunt to the independent advisor and therefore he cannot condone that decision."
Just before the debate later today, deputy prime minister Clegg will appear at the Leveson Inquiry into media ethics and standards to discuss the relationship between politicians and Rupert Murdoch.
Tomorrow, Cameron will give evidence to the inquiry, where he is expected to be quizzed on the decision to hand the review of Murdoch's bid for Sky to Hunt, despite it being known that the culture secretary was at the least "sympathetic" to the proposed takeover.