Unity Investments, a vehicle controlled by Baugur, bought into Debenhams last month with an initial 4.87 per cent stake.
The move has also prompted City analysts to speculate a possible merger between House of Fraser and Debenhams. Baugur increased its stake in House of Fraser to 9.5 per cent before buying the store last August.
Kaupthing Singer & Friedlander analyst Matthew McEachran said: 'Given their track record for buying and merging firms, it is a definite possibility. However, from a House of Fraser standpoint, it looks too early to enter into another round of consolidation.'
Debenhams, which in April issued a third profit warning since its floatation last year, is thought to be in talks with several other European retailers about a possible merger.