The property group started building a holding in Selfridges in August. The company, led by John Ritblat, refused to clarify its intentions towards Selfridges saying only that it has built the stake "for investment purposes".
Analysts have been sceptical about the possibility of a bid but say British Land might be interested in a sale and leaseback of Selfridges' valuable site on London's Oxford Street. According to BT Alex.Brown, Selfridges underlying asset value is 214p per share.
Selfridges has proved a volatile investment since its demerger from Sears last summer. But earlier this week it offered shareholders some reassurance when it issued a solid Christmas trading statement.
Sears, meanwhile, is battling against a hostile pounds 520m bid from a company fronted by Philip Green, the retail entrepreneur, and backed by the secretive Barclay Brothers.