Poundworld offers around 8,000 product lines mostly priced at Â£1, including groceries, toiletries, household cleaning and confectionery items.
The business operates from 335 stores and its head office and distribution centre in Normanton, near Wakefield in West Yorkshire.
The business employs around 5,100 people at its many sites, including stores in Preston city centre, St George's shopping centre and Deepdale Shopping Park
Deloitte said Poundworld would continue to trade while a buyer for all or part of the business is sought.
There are no redundancies or store closures at this time.
Like many high street retailers, Poundworld has suffered from high product cost inflation, decreasing footfall, weaker consumer confidence and an increasingly competitive discount retail market.
Clare Boardman, joint administrator, comments: “The retail trading environment in the UK remains extremely challenging and Poundworld has been seeking to address this through a restructure of its business.
"Unfortunately, this has not been possible. We still believe a buyer can be found for the business or at least part of it and we are keeping staff appraised of developments as they happen.
"We thank all employees for their support at this difficult time.”
Dave Gill - Usdaw National Officer said: “Poundworld staff are deeply concerned about their jobs after the company failed to secure a rescue package. We are seeking urgent talks with the administrators to represent the best interest of our members and urge them to find a buyer for the company.
“Regrettably Poundworld do not recognise Usdaw and they have not been keeping us informed of developments. We are hopeful that the administrators will engage with us to help save jobs. We welcome Deloitte’s initial approach for Poundworld to continue to trade while a buyer for all or part of the business is sought and that there are no redundancies or store closures at this time.
“Usdaw is providing the support and advice our members require at this very difficult time and we expect the administrators to ensure all staff are treated with dignity and are fully consulted.”