Green's reputation was dented by the collapse of Allders. However, taking on the Croydon shop (pictured), which has a 31-year lease from former owner Minerva, would offer Green an immediate opportunity to restore his name.
Green refused to comment on the speculation, but is understood to be considering a number of options.
A spokesman for administrator Kroll said the famous North End store was one of 10 that remained on the block after Bhs, Debenhams and Primark walked away with 24 shops - the prize chunk of the estate - earlier this week. He said most remaining bidders were looking at one or two stores.
The Croydon shop, once the jewel in Allders' crown, is likely to struggle to find a tenant, because it is the subject of redevelopment plans and therefore may only have a limited shelf life.
Allders' Croydon store is the third-largest shop in the UK, trading from 340,000 sq ft (31,585 sq m), with a gross area of 500,000 sq ft (46,450 sq m). Former Allders managing director Stan Kaufman said the store took more than£100 million in its heyday, but that a lot would depend on whether Green could retain the right to the name.
Green's predecessor, Harvey Lipsith, is also keen to use the name if he succeeds in acquiring some of the stores.
'Allders is a powerful, powerful name in Croydon,' said Kaufman. 'It is like Harrods or Selfridges, but if he called it Green's of Croydon he might be in trouble. He would have to pay very little for it in my view, because the running costs are high.'
Allders boost for Bhs
Allders' demise has proved an opportunity for Philip Green's Bhs chain. The entrepreneur will establish a spin-off Bhs home furnishing arm with the 10 stores he acquired in the auction of the collapsed department store's estate.
Green's new chain could fill the void left by Allders, which was once famous for its home offer. Green said he had not decided on the fascia yet, but said the move 'was something he had been thinking about for some time'. He aims to have the converted stores open by the summer and the offer would include furniture, beds and carpets.