The holding makes it Woolworths' biggest shareholder, with its shares worth about£36 million.
Word that WHSmith was to launch an improbable bid for Woolworths swept the Square Mile on Tuesday. However, Baugur has been more persistently linked with the retailer. It already owns Oasis, Karen Millen, Jane Norman, Hamleys and MK:One.
Baugur has built up large stakes in several British retailers, which have sometimes proven a prelude to a bid. It has also made millions by buying and then selling stakes in retailers such as Selfridges, House of Fraser, Mothercare and JJB Sports.
Chief executive Jón Ásgeir Jóhannesson commented recently that Woolworths was 'good value at these prices'.
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