Sir Christopher Kelly had questioned whether the new rules went far enough
The committee on standards in public life is considering its own inquiry into MPs' expenses, the BBC understands.
Sources have indicated that its chairman Sir Christopher Kelly is minded to press for an inquiry.
An MPs' committee carried out a five month inquiry, but their proposals were rejected in a Commons vote on Thursday.
Lib Dem leader Nick Clegg says he will submit his MPs' expenses to independent spot checks, regardless of the vote.
Mr Clegg said the party would work with the Institute of Chartered Accountants to draw up detailed proposals on how it would work.
And he said his frontbench team would begin publishing quarterly breakdowns of their expenses claims.
'Very damaging week'
He said: "The Liberal Democrats will now implement as many of the recommendations as we can to tighten up the rules on MPs' expenses - particularly those relating to spot checks of MPs' expense claims."
"I hope that Gordon Brown and David Cameron will join me in implementing these measures so that together we can begin to restore public confidence in politicians after what has been a very damaging week."
Neither Mr Clegg nor Mr Brown were in the Commons for the vote as both were at meetings, however no Lib Dems MPs voted to keep the system as it was.
The BBC understands an inquiry by the committee on standards in public life - set up to monitor standards in public life as a response to perceptions of "sleaze" in government and public affairs - would extend beyond the housing allowance and cover all MPs' expenses.
Its chairman, Sir Christopher, has previously said he was "baffled" MPs thought it appropriate to carry out their own review and has said he would launch his own inquiry if it did not address public concerns.
And last week he warned MPs that the reforms suggested by the Members Estimate Committee - thrown out by MPs on Thursday - may not go far enough.
On Thursday MPs voted by a majority of 28 to retain the additional costs allowance - used to fund MPs' second homes - and to have their spending looked at only by internal, rather than external, auditors.
More than half of the 646 MPs did not take part in the contentious vote. Of the 172 who voted to keep the old system of allowances, subjected to internal audits, 146 were Labour MPs, of which 33 were government ministers.
The shadow cabinet voted for the reforms and Conservative leader David Cameron earlier criticised Gordon Brown for not turning up to the vote.
He said the Conservatives had been in favour of reform and transparency while the government "was basically saying 'let's be against reform, let's keep the John Lewis list and let's not sort this out'".
He added: "And it was extraordinary that the prime minister chose not to come and vote. And now he says, apparently, he's disappointed with the result. Well if he was disappointed, why didn't he vote?
"Why was it that his whips were pointing people into the wrong voting lobby?"
Mr Brown's spokesman said he had been in meetings and had been updated with the progress of the debate and denied he had "ducked" the vote.
The prime minister told the BBC later he also thought the issue needed revisiting.
"I was not happy with what happened. I am very disappointed about the vote," he said.
"We voted to keep the pay of Members of Parliament down below some of the settlements in the public sector but we've got to look at the issue of transparency and accountability and expenses again.
"I'm disappointed but I believe we can make progress again."