The retailer will meet Malcolm Walker to further discuss the bid for its 820 stores, British newspapers reported on Sunday.
Walker is part of a consortium including Hamleys parent company, Baugur, which currently owns a ten per cent stake in the retailer.
The consortium is not interested in Woolworths's EUK and 2 Entertain distribution businesses and had an initial bid rejected earlier this month.
The Observer said the approach was an "opening shot" and Walker would meet Woolworths chairman Richard North in the coming week.
The Sunday Times said Walker would slash overheads and considerably narrow the product range at Woolworths, which offers sweets, toys and DVDs.
Woolworths shares, which have lost two thirds of their value over the past year, closed at 7.08 pence on Friday to value the business at £105 million.
Woolworths said last week that it "was not unwilling to talk to Baugur" after rejecting an approach of about 50 million pounds.