MPs would have to hand back second home profits under the plans
Proposed reforms of MPs' expenses are in doubt after the head of the body charged with rewriting the rules said he might not implement them all.
The Daily Telegraph said Prof Sir Ian Kennedy was unhappy with standards watchdog Sir Christopher Kelly's plans.
Sir Ian was also quoted as saying he had "no obligation" to accept them.
Labour MP John Mann said the remarks, if true, were "totally unacceptable" and if Sir Ian was "intending to unravel Kelly, he should resign".
Mr Mann said that while Sir Ian was required to conduct a consultation on the reforms, it was the understanding that he would accept the Kelly proposals.
Sir Christopher set out his plan to reform expenses on Wednesday and received the backing of the three main party leaders at Westminster.
His report has now gone to the new Independent Parliamentary Standards Authority (Ipsa) - headed by academic lawyer Sir Ian - which is charged with drawing up the final expenses regime.
When he started his work on Wednesday, Sir Ian said the Kelly report provided a "clear set of recommendations for reform".
But the Telegraph said on Saturday that Sir Ian was unhappy with some of them, including the move to compel MPs to return any capital gains made from the sale of second homes to the taxpayer.
He was also reportedly concerned about the proposal to ban MPs from employing relatives on their payroll.
A spokesman for Ipsa said it had "a statutory requirement to consult on the content of a new allowances scheme".
"Sir Ian made his position clear when he was nominated as chair - Ipsa's job is to take the reins following the Kelly report and put together a scheme for consulting on," he said.
But BBC political correspondent Ross Hawkins said that if Ipsa was seen to let Sir Christopher's ideas slip away, it would re-open the furious debate about expenses which many MPs hoped was finally drawing to close.
No more 'flipping'
Sir Christopher announced a series of other plans to overhaul the expenses system, including:
- Ending claims for mortgage interest payments on second homes - instead MPs will only be able to claim for rent or hotel stays.
- Banning the "flipping" of residences, with the designation of main and second homes to be governed by an objective test and "robustly" enforced by a new independent regulator.
- Scrapping generous resettlement grants for MPs retiring or standing down voluntarily, of up to £65,000 - they will receive eight weeks' pay instead.
- Ending the right to claim for gardening and cleaning costs and introducing the requirement for any MP able to commute to do so.
MPs will not get a vote on the reforms, but several are expected to challenge the ban on employing relatives.
The union Unite, acting on behalf of some spouses, is already considering whether it can seek a judicial review of the decision.
Sir Christopher, however, said his proposals were "reasonable and fair" and would ensure MPs were "properly supported" while providing stronger safeguards for the taxpayer.
Gordon Brown's spokesman said last week Ipsa did have the power to take the Kelly recommendations and "shape" them further - a remark Sir Christopher later said he was "mystified" by.
Speaking to the BBC, Mr Baker said: "Well, I'm deeply dismayed to be quite honest if his comments are accurately reported.
"The package that Christopher Kelly put together is a good package. It's been well received by the public at large - MPs, I think, were prepared to swallow it [and] the three party leaders have got behind it."
The Telegraph said Sir Ian was concerned there could be legal challenges to the new rules, but Mr Baker said he hoped the Ipsa chairman would only "tweak them at the edges to take account of those sorts of issues rather than re-writing them".
"If he's going to abandon the ban on spouses and allow MPs to continue with mortgages, that rips the heart out of what Christopher Kelly said - there's not very much left after that.
'Price of a fridge'
"It will fuel suspicion, I'm afraid, amongst the public at large that, just as this matter was being put to bed, here is another behind-the-scenes stitch-up," he said.
But Labour MP Stuart Bell, who sits on the Commons' Members Estimates Committee, said public trust could be restored because the final expenses proposals eventually laid before Parliament by Ipsa would be "absolute".
"MPs will never again have any say over their allowances," he told the BBC.
"We have MPs now arguing about the price of a fridge. It gets to the absurd and the sooner we get away from that the public will get their confidence back and Parliament will get on with the role that it's supposed to do, holding the executive to account."
Sir Alistair Graham, the former chairman of the Committee on Standards in Public Life, told the BBC that any move to abandon plans to make MPs pay back capital gains was "inconceivable".
"That's precisely what the public wants - that MPs should not make any personal gain out of having received public funds to carry out their duties," he said.
Sir Alistair also added: "It's most unfortunate if Sir Ian has started off-the-record sniping at Sir Christopher Kelly's report."