It comes just a day after Sir Philip's retail empire was revealed to be on the brink of collapse with around 15,000 jobs at risk.
The offer from Frasers Group, which runs Sports Direct and House of Fraser, amounts to £50 million likely to be in the form of a secured loan, Sky News reported on Saturday.
The broadcaster 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."
But the PA news agency understands there has been no formal approach to Arcadia.
The group 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 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.