Stephen Timms, the head of the Work and Pensions Committee, called on the tycoon to stump up funds as he urged the Pensions Regulator watchdog to protect pension scheme members.
Mr Timms also asked about the status of a £385 million package that was agreed between the regulator, Arcadia and the group’s owner last year.
If the group, which has brands including Topshop, Dorothy Perkins and Burton, enters administration, its pension scheme would be taken on by the Pension Protection Fund.
Arcadia’s pension deficit, which is estimated to be as much as £350 million, raises risks that some workers could lose out.
Mr Timms called on the Green family to use their personal wealth to cover the shortfall.
He said: “There is unquestionably a moral case for the Green family to do the right thing and guarantee Arcadia’s hardworking staff what is rightfully theirs, whatever happens this Christmas.
“But the Pensions Regulator must also ensure that it is doing everything in its power to fight the corner of the pension scheme members.
“This is a crucial moment for the regulator to show that it has learned the lessons of previous corporate collapses, such as those of BHS and British Steel.”
The comments come as Mike Ashley’s Frasers Group confirmed an offer for a £50 million lifeline has been rejected.
In a statement to the London Stock Exchange, the company said: “Frasers Group can confirm that Arcadia Group Limited have declined Frasers Group’s offer of a lifeline loan of up to £50 million.
“Frasers Group were not given any reasons for the rejection, nor did Frasers Group have any engagement from Arcadia before the loan was declined.”
It's understood Arcadia Group will enter administration on Monday with Deloitte to be appointed as administrators in the coming days.
The UK taxman could also lose out if the company goes bust on Monday.
It would come ahead of new rules next month which would make HMRC a preferential creditor and improve its chances of securing substantial revenue from the retail group’s insolvency.
The rejected offer from Frasers Group, which runs Sports Direct and House of Fraser, amounts to a £50 million loan, Mr Ashley’s company confirmed.
Frasers Group said: “The company can confirm that it has made an offer and provided draft terms to the Arcadia Group for a loan of up to £50 million and is now awaiting a substantive response.
“Should the company and the Arcadia Group’s efforts to agree an emergency funding package fail and the Arcadia Group enter into administration, the company would be interested in participating in any sale process.”
Sky News quoted Chris Wootton, Frasers’ chief financial officer, as saying: “We hope that Sir Philip Green and the Arcadia Group will contact us today to discuss how we can support them and help save as many jobs as possible.”
Arcadia had been in emergency talks with lenders in a bid to secure a £30 million loan to help shore up its finances.
If the insolvency is confirmed, it is expected to trigger a scramble among creditors to get control of company assets.
It is estimated that around £250 million worth of supplier invoices to Arcadia could go unpaid if there is no rescue deal, according to insurance specialists Nimbla.
The company said this could have a ripple effect which could “threaten the existence of hundreds of small businesses and jobs” further down the supply chain.
It is the latest retailer to have been hammered by the closure of stores in the face of coronavirus, with rivals including Debenhams, Edinburgh Woollen Mill Group and Oasis Warehouse all sliding into insolvency since the pandemic struck in March.
The group has more than 500 retail stores across the UK, with the majority of these currently shut as a result of England’s second national lockdown, which will end next week.
Earlier this year, Arcadia revealed plans to cut around 500 of its 2,500 head office jobs amid a restructure in the face of the coronavirus crisis.