Woolworths stores are still open at present
There has been "strong interest" in buying the leases of Woolworths' 815 stores across the country, administrator Deloitte has said.
The comment came as a 1600 GMT Thursday deadline passed for potential buyers to register their interest in taking on various numbers of the shops.
Deloitte said nothing had yet been decided, and it was continuing talks to sell Woolworths as a going concern.
It said "a number of parties" were interested in buying the whole firm.
However, the BBC understands it is unlikely that any buyer will take on the entire business, and instead will only be interested in buying the most profitable stores.
This would leave a number of shops to be sold to other buyers.
There is no deadline to the talks to buy Woolworths as a going concern.
Woolworths went into administration on 26 November, and has debts of £385m.
At present the stores are continuing to trade.
Woolworths' CD, DVD and computer games distribution business Entertainment UK is also in administration.
However, publisher 2 Entertain, its joint venture with BBC Worldwide, in which Woolworths has a 40% stake, continues to operate as normal.