Woolworths owns 40% of 2entertain, which publishes DVDs including 'Doctor Who' and 'Blue Planet', the rest is owned by BBC Worldwide.
The sale, which would raise around £100m, is understood to be crucial to preventing Woolworths going into administration.
The company's directors are also trying to reach a deal with Hilco UK, the US restructuring specialist that has offered to buy its 840-store retail business and take on a large part of the company's debt.
This would leave the company with a profitable wholesale distribution operation and allow it to remain in public ownership.
However, both deals depend on the approval of the lenders of the company's £385m debt. The lead creditors are Bank of Ireland subsidiary Burdale Financial and GMAC Commercial.
If the lenders block the deal, Woolworths directors fear they will have to put the company into administration to avoid breaking the law on trading while insolvent.
The Times reports that suppliers have refused to trade with the company and its till receipts have fallen.
Woolworths opened its first store in Britain in 1909 in Liverpool. It began life in America where Frank Woolworth began business in 1879. The US and UK businesses split in 1982 when the British Woolworths was acquired by Paternoster Stores, the forerunner of Kingfisher.
Woolworths is not alone in being on the brink of administration. Furniture retailer MFI is understood to have only days to resolve a problem with landlords over unpaid rents.