Woolworths have seen their shares increase after the troubled retailer said it had rejected a takeover bid for its 815 stores from Iceland.
The offer from a consortium headed by Mr Walker of Iceland, was considered too low. Icelandic investment group, Baugur, has a 10% stake in Woolworths and also owns Iceland.
Mr Walker intends to take control of Woolworths' retail sites, but only if the firm agrees to cover its pension deficit, valued at £48.2m in its latest annual report, and retains its £142m debt.
To Woolworths' board the offer undervalued its assets and involved a complex and unachievable restructuring.
Mr Walker's bid does not include the retailer's EUK business, which provides music and DVDs to other retailers, or its joint publishing venture with the BBC, 2 entertain.
It is thought that Woolworths is now even more attractive to those willing to bid for a takeover.
The homeware-to-toys chain has suffered as the economic slowdown has affected consumer spending.
