William Wragg said he will speak to a Scotland Yard detective in the House of Commons early next week, raising the prospect that police could open an investigation.
Downing Street has said it will not mount its own inquiry into the claims, despite calls to do so by both Conservative and opposition MPs.
A No 10 spokesman said it would open an inquiry only if it was presented with evidence to back up Mr Wragg’s assertions.
Mr Wragg, who is chairman of the Commons Public Administration and Constitutional Affairs Committee, said he believed an investigation should be for the “experts” in the police.
Chris Bryant, the senior MP who leads the Commons sleaze watchdog, said on Saturday that Government attempts to pressure Tory MPs seeking to oust Boris Johnson are illegal.
Mr Bryant, chairman of the Commons Standards Committee, said that threats to withdraw public funding from MPs’ constituencies amounted to “misconduct in public office” and should be referred to the police.
Mr Bryant, an opposition Labour MP, said he had spoken to “about a dozen” Conservatives in recent days who had either been threatened by Government whips with having funding cut from their constituencies or promised funding if they voted “the right way”.
“I have even heard MPs alleging that the prime minister himself has been doing this. What I have said to all of those people is that I think that is misconduct in public office,” he said.
“We don’t run a ‘pork barrel’ system. It is illegal,” Mr Bryant said. “We are meant to operate as MPs without fear or favour.
“The allocation of taxpayer funding to constituencies should be according to need, not according to the need to keep the Prime Minister in his job.”
A Metropolitan Police spokesman said: “As with any such allegations, should a criminal offence be reported to the Met, it would be considered.”
Inquiry into lockdown parties
Mr Wragg’s latest intervention comes as No 10 is braced for the expected delivery next week of the report of Sue Gray, the senior civil servant investigating lockdown parties in Downing St elsewhere in Whitehall.
It is likely to lead to renewed calls from opposition parties for a police investigation if there is any evidence Covid-19 rules were broken at events that include a gathering in May 2020 attended by Mr Johnson.
Opposition MPs are piling on pressure to ensure the full report is published after suggestions that only see the findings from the investigation will be released.
“Boris Johnson cannot be allowed to cover up or obscure any of the truth when he has insisted on a hugely protracted internal probe to tell him which parties he attended and what happened in his own home,” said Labour deputy leader Angela Rayner.
“The Sue Gray report must be published in its entirety with all accompanying evidence.”
Mr Wragg is one of seven Conservative MPs to have called publicly for the prime minister to resign. He stunned Westminster with allegations this week of a campaign of intimidation by No 10 that amounts to criminal conduct.
He said Conservative MPs trying to trigger a no-confidence vote in Mr Johnson had been told public funding for projects in their constituencies would be cut off and threatened with stories in the press to embarrass them.
Christian Wakeford, the Bury South MP who defected to Labour, later described how the Tory whips had threatened to withdraw funding for a new high school in his constituency if he rebelled in a vote over free school meals.
Report could be next pressure point
Ministers have sought to dismiss the allegations, insisting the whips had no role in the allocation of public funding.
Business Secretary Kwasi Kwarteng acknowledged on Friday that Mr Wakeford’s allegation was “very serious” and said he was “sure” it would be investigated.
But a spokesman for the prime minister said: “We’re not aware of any evidence to support what are clearly serious allegations.
“If there was any evidence to support it, it would of course be looked at.”
The latest disclosures will only fuel the febrile mood at Westminster, with Mr Johnson’s political survival hanging in the balance.
Mr Wakeford’s defection appeared to have put the plotting on hold as Tory MPs publicly rallied behind the leadership, while the rebels largely went to ground.
But the publication of Ms Gray’s report represents another moment of danger, potentially prompting a wave of letters to the chairman of the Tory back bench 1922 Committee, Sir Graham Brady.
Under party rules, there will be a confidence vote in Mr Johnson if 54 of the party’s MPs write to Mr Brady to call for one.
Mr Johnson is expected to spend the weekend at Chequers, his official country residence, ringing round potential rebels urging them not to plunge the dagger.
The Times reported the prime minister had reassembled the ministerial team which helped him mount his successful leadership bid in 2019 as he seeks to shore up support.
Transport Secretary Grant Shapps is playing a role in the operation with three former whips and other loyalists, it reported.