Card Factory owner Charterhouse has shelved plans to sell the 650-store retailer after receiving bids below its expectations.
The private equity firm will instead focus on a refinancing ahead of a possible initial public offering, The Financial Times reported.
The retailer was estimated to be worth more than £500m including debt.
Private equity firm Charterhouse acquired the retailer in 2010 in a deal reportedly worth more than £350m.
Card Factory is led by chief executive Richard Hayes and he has ambitious plans to double the number of stores in the long term to 1,200.
Late last year Charterhouse appointed Ernst & Young to look at its options including a possible float on the stock exchange.