Property tycoon Ardeshir Naghshineh says Woolworths should instead look at making money by selling off some of its 840 UK stores.
The £1 offer is said to come from restructuring firm Hilco, although there has been no confirmation that such an offer has been made.
Hilco would have to agree how much of Woolworth's £385m debt to take on.
Without some form of a deal, analysts say Woolworths faces the real risk of going into administration and up to 20,000 jobs could be lost.
"Quite a lot of retailers now want to expand on the UK High Street," said Naghshineh.
"If marketed properly, further afield, overseas, you'll probably get better value for them [the stores]."