Maria Miller has been warned accepting a £17,000 pay-off would be a "further insult" to the taxpayer and she should turn it down.
The former Culture Secretary is entitled to three months' pay on leaving her post under law, however, she can refuse the amount.
The sum is significantly more than the £5,800 she has been ordered to repay in wrongly-claimed expenses and the Labour MP John Mann has said that given her conduct the payment would be "inappropriate".
Mrs Miller resigned this morning after a week of mounting pressure following an investigation into the expenses claims she made for a second home.
Mr Mann, who made the initial complaint about her allowances claims, said: "It is a ridiculous and outdated practice to pay off ministers when they return to the backbenches.
"In light of Maria Miller's conduct, it would now be inappropriate for her to claim severance pay following her resignation. For her to accept a payoff would be a further insult to the taxpayer."
Mrs Miller has insisted she was not pushed from her role as Culture Secretary but had to go because the scandal over her expenses was becoming a "distraction".
Maria Miller's 32-second apology in the Commons was incendiary
In an interview after her resignation, a clearly upset Mrs Miller said she took "full responsibility" for her decision to step down.
She said: "This has been a really difficult 16 months. Because I was cleared of the central allegation made about me by a Labour Member of Parliament, I hoped that I could stay. But it has become clear to me in recent days that it has become an enormous distraction.
"It is not right that I am distracting from the incredible achievements of this Government."
She denied she thought there had been a "witch-hunt" against her because of her role overseeing the reforms on press freedom suggested in the Leveson report, as had been claimed by her aide on Tuesday.
Asked if she was sorry, she replied: "I have made it clear and apologised unreservedly to the House of Commons and made sure that it was clear to everybody that I took full responsibility for those findings.
"I want to make that the situation is clear to everybody and make sure that I can move on."
In her resignation letter to David Cameron, Mrs Miller, 48, told him she was "very grateful" for his personal support during the growing row over her expenses.
Mr Cameron repeatedly backed his Culture Secretary
Mr Cameron, who consistently offered public support for his minister, said he was saddened by her departure but hoped the Basingstoke MP could make a return "in due course".
Mrs Miller finally stepped down six days after she was forced to apologise in the House of Commons for her attitude to an inquiry into the allowance claimed on her second home.
The Prime Minister had been under pressure in recent days to sack her from Tory activists and MPs, and Mrs Miller's position had become untenable.
Following criticism over his handling of the case from both Tory and Labour MPs Mr Cameron robustly defended his actions at Prime Minister's Questions.
When Labour leader Ed Miliband asked him what he had learned from the situation, he said: "I hope that one lesson that won't be learned is that the right thing to do as soon as someone has to answer allegations is just to instantly remove them, rather than give them a chance to clear their name and get on with their job.
"If people clear themselves of a serious offence, you let them get on with their job, you let them try to do their job. That is actually the right thing to do.
The second home at the centre of the row
"Firing someone at the first sign of trouble ... that is not actually leadership, that is weakness."
Mrs Miller's camp had, on Tuesday night, attempted a fightback after days of newspaper headlines and the faltering support for her from within Government.
Her aide, Mary Macleod, appeared on Sky News to claim she was a victim of a witch-hunt because she was dealing with press reforms recommended in the Leveson report. She had sent a text to MPs attempting to garner support for Mrs Miller.
She also claimed that Mrs Miller was unpopular because she was responsible for steering through the legislation on gay marriage.
In her resignation letter Mrs Miller said: "Of course, implementing the recommendations made by Lord Justice Leveson on the future of media regulation, following the phone hacking scandals, would always be controversial for the press.
"Working together with you, I believe we struck the right balance between protecting the freedom of the press and ensuring fairness, particularly for victims of press intrusion, to have a clear right of redress."
Mr Cameron has announced that Sajid Javid, MP for Bromsgrove, is to become the new Culture Secretary.
Nicky Morgan will replace him as Financial Secretary to the Treasury and Andrea Leadsom will become Economic Secretary to the Treasury.
Mrs Miller's departure leaves three women in the Cabinet: Home Secretary Theresa May, Northern Ireland Secretary Theresa Villiers, and International Development Secretary Justine Greening. Baroness Warsi sits in the Cabinet as Minister Without Portfolio as is Ms Morgan, in her role.
Conservatives in Mrs Miller's constituency voiced disappointment at her departure.
Stephen Marks, a Conservative councillor on Basingstoke and Deane Borough Council, said: "She did Leveson on press complaints and I feel the press were going to get their own back on her. I am saddened that she had to resign, but that is the way it is."
Mrs Miller issued a much-derided 32-second apology on Thursday after Parliament's sleaze watchdog upbraided her for her attitude to an expenses inquiry into claims for a second home.
She was also ordered to pay back £5,800 of wrongly-claimed allowances on the house in Wimbledon, southwest London, which she sold for a £1.2m profit in February.
However, it emerged that the Commissioner for Parliamentary Standards had found that Mrs Miller should have paid back £45,000 in expenses claimed on the home but this was overruled by the Standards Committee of 10 MPs and three independent members, who do not have a vote.
It led to calls for an end to a system where MPs are allowed to police their own expenses, with the head of the Independent Parliamentary Standards Authority, Sir Ian Kennedy, saying they should not "mark their own homework".