The privately-owned knitwear chain is said to be in advanced talks to acquire Jane Norman, which went into administration putting 1,600 jobs at risk.
Debenhams and Aurora Fashions, which owns Oasis, Coast and Warehouse, are also thought to be interested in buying all or parts of the chain.
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Hide AdCommentators have said Edinburgh Woollen Mill's bid has come as a surprise, as it targets men and women aged 45 and over, while Jane Norman targets customers aged 16 to 25.
However, the firm has a history of acquiring failing retailers and turning their fortunes around.