Poundworld filed a notice of intention to appoint administrators last Thursday and this has given it 10 days to continue talks aimed at negotiating a sale, the spokesperson confirmed.
Private equity firm Alteri Investors, whose website says it specialises in "challenging retail situations", was in advanced discussions with Poundworld's owner TPG.
Poundworld founder Chris Edwards is said to have been attempting to put together a rescue bid for a chunk of the company.
If a solvent sale of Poundworld cannot be agreed, the business could be sold through a pre-pack administration or collapse outright, underlining the urgency of rescue talks which are being led by Deloitte, the professional services firm.
Poundworld had previously rejected offers to sell through a pre-pack but all options are now being considered.
Deloitte has been preparing contingency plans for an administration in the event of takeover talks collapsing.
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The stores suffered a major rise in multi-million pound losses previous year - rising from £5.4m to £17.1m in 2016/17.
Mr Edwards, who pocketed an estimated £75 million from the deal with TPG, has since been appointed to run Poundstretcher, which has also experienced hard trading.
In May it emerged that TPG had made a decision to cut it losses and was putting Poundworld, which started in 1974 as a market stall in Wakefield in West Yorkshire, up for sale.
It also has a Poundworld Plus outlet at the Peel Centre, Dumfries.
Retailers Maplins, Toys "R" Us, Mothercare, Carpetright, plus a string of restaurant chains, have hit the headlines this year because of trading trouble.