Maria Miller has indicated she expects to pay thousands of pounds in capital gains tax after making a £1.2 million profit on a home that was part-funded by the taxpayer.
Aides to the Culture Secretary said she would not seek to dodge a bill amid continuing demands for her resignation.
Last week the cross-party Commons Standards Committee ordered Mrs Miller to say sorry and repay £5,800 in overclaimed mortgage expenses - £40,000 less than an independent report had recommended.
Mrs Miller was condemned for giving a "contemptuous" 32-second apology on the floor of the House.
David Cameron again defended his Cabinet minister this morning, insisting she was doing a "good job".
But he also said he was "very open" to looking at ways of improving the policing system for MPs, after criticism that they are still able to "mark their own homework".
Mrs Miller sold the property in Wimbledon, south London, in February for just under £1.5 million, having purchased it in 1996 for £234,000.
Between 2005 and 2009 she declared it as her second home for expenses purposes and claimed around £90,000 in mortgage and running costs - almost the maximum allowed.
A spokeswoman for the Culture Secretary dismissed suggestions that she would attempt to avoid a capital gains tax (CGT) bill by arguing that it had been her main home throughout the period.
The aide said it was "common knowledge" that the London house had been Mrs Miller's second home between 2005 and 2009.
"HMRC (Her Majesty's Revenue and Customs) will present her with a bill," the spokeswoman said.
"There is no hiding anything here."
Profits on the sale of a primary home are generally exempt from CGT, but HMRC will calculate a liability based on any time in which the property was used as a second residence.
If Mrs Miller declares that had been the case with the Wimbledon property for four years, she could potentially face a charge of tens of thousands of pounds.
Labour has made a formal complaint to Kevin Barron, chairman of the standards committee, about the way Tory MP Mrs Miller apologised for failing to cooperate fully with Ms Hudson's investigation.
"This was inadequate to the point of being contemptuous of your Committee's report and the Members' Code of Conduct," backbencher Sheila Gilmore wrote.
During a visit to Asda in Clapham, south London, Mr Cameron was asked about polling which showed most Conservatives believed Mrs Miller should be out of a job.
"What matters is doing the right thing. I think Maria has done the right thing by repaying the money, making an apology and now getting on with her job," he said.
"We ought to remember she was found innocent of the claim that was levelled at her at the start of this process.
"I think that is important to bear in mind."
Asked if Mrs Miller was still in her post because she was a state-educated woman, he replied: "Maria Miller is in her job because she is doing a good job as Culture Secretary."
Mr Cameron said reforms to the expenses system that brought in Ipsa were "very important" changes.
"If there are further changes that people think are appropriate, I'm very open to suggestions," he added.
Tory MP Nicola Blackwood - a ministerial aide - said Mrs Miller was faced with "most serious" questions and her response could have been "clearer".
"The questions which she is being faced with are of the most serious and I have to say when I deal with my expenses I am as transparent as I can be, it's all up on my website," she told BBC Radio Oxford.
"I have to say if I was faced with the kind of questions that she is faced with I would be really quite worried indeed.
"I only know what has been reported in the papers... but clearly it's very unhelpful for this to drag on in the way that it is."
Asked about Mrs Miller's response to the controversy, she adds: "It would be helpful if it was clearer."
The spokeswoman for Mrs Miller said: "It is well documented that Maria stopped claiming any accommodation allowance at all in April 2009.
"The sale of the Wimbledon property in February falls in a tax year that has not yet been assessed.
She will of course deal with the matter in accordance with HM Revenue and Customs rules and pay any tax that is due."
As a higher rate taxpayer, Mrs Miller would be liable for CGT at 28%.
An estimated profit of £1.2 million on the London property could leave her owing around £70,000 to HMRC for the four year period in which she claimed expenses - although other allowances are likely to reduce that figure.
Commons Speaker John Bercow rejected a call for a Government minister to be summoned to the House to answer questions about the future of the Standards Committee.
Labour MP John Mann, whose complaint sparked the commissioner's investigation into Mrs Miller's claims, had asked for an urgent question on reform of the system.
Mr Mann said the Standards Committee had "no credibility whatsoever".
He said: "The general public is pretty much unanimous, if not totally unanimous, that MPs should not sit in judgment on themselves. I totally agree.
"The longer Parliament delays sorting this out, the worse it is for our democracy and the institution of Parliament.
"Having the committee overrule the independent commissioner means this committee has no credibility whatsoever. Its power to sit in judgment over fellow MPs should now be removed.
"The sooner the penny drops, the better."
Mr Mann, who has called for Mrs Miller's resignation, added: "The question I'm getting all the time is 'what has happened to honour in British politics?'"
Attorney General Dominic Grieve told BBC Radio 4's The World At One: "I can't answer on Maria Miller's behalf. The Prime Minister has explained his position and I don't think I have anything to add.
"She is a valued colleague, as far as I am concerned. She has got to answer to her constituents and also answer for her responsibilities to the Prime Minister."
Mr Grieve said Parliament had already made significant changes with the creation of the Independent Parliamentary Standards Authority (Ipsa) - which now handles MPs' expenses - and warned that any further changes could raise important constitutional issues.
"There has always been a tension between maintaining Parliament's independence and placing it under somebody else's scrutiny," he said.
"I don't think that it needs me to explain that there is quite an interesting constitutional issue here. It's one which I think we've been wrestling with.
"In setting up Ipsa, Parliament moved very substantially away from the earlier model of its regulation.
It's very much a matter for my parliamentary colleagues if they think that further change is going to be needed.
"I think that we need to evaluate that further change probably on how the system is working today, and not necessarily with reference to events that are 10 years old."