Sky News reports that the two state-controlled lenders - who took charge of the business two years ago - are currently on the lookout for potential suitors.
The news provider noted that people familiar with the matter believe a price tag of around Â£25 million ($41 million) will be placed on the retailer, which has nearly 100 premises in the UK.
Advisory firm Cavendish Corporate Finance - an organisation founded in 1988 that has advised on around 400 company sales - is likely to oversee the auction, although this is yet to be confirmed.
Robert Dyas - which has a history stretching back to 1872 and a workforce of around 1,000 people - is the latest high street name to come into difficulty following similar scenarios for groups such as HMV and Mothercare.
By Tony Aynsley