Poundstretcher's owners are talking to private equity firm Endless about a possible sale of the business, according to reports.
Crown Crest group, which controls Poundstretcher, is owned by brothers Aziz and Rashid Tayub, who, according to the Sunday Times, took Endless on a tour of Poundstretcher last month.
It is thought that the Tayub brothers are also in talks with TJ Morris, the owner of Home Bargains, about the future of Poundstretcher, which has been under pressure since the devaluation of sterling following the outcome of the EU referendum in June last year.
If Endless steps in to save Poundstretcher, it would be the second high-profile takeover for the firm so far this year.
In March, Jones Bootmaker was bought up by Endless in a £10.5m deal. The shoe retailer, which had a workforce of 1,100 people, was put into administration by its former owner Alteri Partners.
Endless' acquisition of Jones Bootmaker resulted in the loss of 262 jobs.
The German discount supermarkets have been performing strongly following the Brexit vote as shoppers seek to avoid the impact of food price inflation.
However, discounters in other segments of the retail industry have not fared so well. Cut price shoe maker Brantano went into administration towards the end of March, and five days later Poundland announced it was putting a handful of its 99p stores into administration.