Clintons could kickstart a major restructure of its Birthdays business if a buyer is not found for the discount card specialist.
Birthdays, which has 141 stores, is not expected to attract much interest from would-be suitors, according to The Independent.
Birthdays has not made a profit since it was acquired by Clintons for £50m in 2004.
Restructuring specialists at Ernst & Young were hired this month to seek a sale for the discount chain. Clintons may have to offload large numbers of stores as part of a formal restructuring of Birthdays.
The discount specialist is understood to be a key part of the strategic review being carried out by Clintons chief executive Darcy Willson-Rymer, who joined the retail group in October.
The review is due to conclude in April. Clintons has appointed Rothschild to help with its strategy.