Mark Francois, the chair of a group of Eurosceptic Tories, said its “strong recommendation” was for Tory MPs to reject the deal.
He told reporters around 30 Tory MPs had attended a meeting earlier to discuss the group’s position, and none had opposed the decision to vote against. However, the scale of the rebellion remains unclear.
He also said former Conservative leader Sir Iain Duncan Smith opposed the deal. Sir Iain himself earlier said he had not yet decided.
Mr Sunak’s government is still expected to win the vote with the support of Labour, which backs the agreement.
The vote is on a key part of the deal, known as the Stormont brake, that aims to give a future Northern Ireland Assembly a greater say on how EU laws apply to Northern Ireland.
Under the emergency mechanism assembly members could formally raise concerns over new EU goods legislation, potentially leading to the suspension of the law and arbitration with the EU.
The vote is likely to be the only vote MPs get on Mr Sunak’s renegotiated deal, known as the Windsor Framework.
The original Brexit withdrawal deal negotiated by Mr Johnson introduced a series of checks on goods sent from Great Britain to Northern Ireland, in order to avoid a border with the Irish Republic.
Despite originally billing the agreement as a “great deal for our country,” Mr Johnson went on to join Tory Brexiters in bemoaning the economic impact of the checks it introduced.
The changes negotiated by Mr Sunak aim to streamline the checks process, which have also proved highly unpopular among unionists in Northern Ireland.
Mr Sunak has said the agreement is the “best deal for the people and businesses of Northern Ireland,” and will boost the region’s economy.
But in a statement issued earlier, Mr Johnson said it was “unacceptable”.
“The proposed arrangements would mean either that Northern Ireland remained captured by the EU legal order – and was increasingly divergent from the rest of the UK – or they would mean that the whole of the U.K. was unable properly to diverge and take advantage of Brexit,” he added.
He said it would be better to proceed with controversial legislation giving British ministers the power to override the original deal, which Mr Sunak has shelved due to his new agreement.
Ms Truss is also said to believe the new framework “fatally impinges” on the UK’s ability to diverge from EU rules.
Leader Sir Jeffrey Donaldson said he will continue to work with the government on “outstanding issues” – even though Downing Street said there are no plans for any substantial change to the deal.
The European Research Group (ERG) of Eurosceptic Tory MPs has criticised the Stormont brake, with legal experts advising them it was “practically useless”.
The deputy chairman of the group, David Jones, said he would be voting against the deal.
But when asked if the ERG would take a unified position on the deal in Wednesday’s vote, he said: “We are not Stalinist.”
The vote will take place during Mr Johnson’s testimony before the Privileges Committee on Wednesday, where he will be quizzed by MPs over Partygate – a day after he admitted misleading Parliament by accident.