MK One racked up losses of £17.4 million last year and has struggled to compete with the supermarkets and Primark. One source close to the situation said: "It's no secret that the value market is having a tough time. MK One is the only value retailer in Baugur's portfolio so maybe there is someone else with other similar value chains who could get more out of it."
Baugur is understood to have already received some interest in the business.
Baugur acquired MK One for £55m in 2004.