TPG is reportedly in advanced talks to buy Poundworld in a deal that could be worth more than £120m.
The US-based private equity firm has been in discussions to purchase the retailer for more than a month, according to Sky News.
It is understood that a number of other private equity firms, including Apax Partners and CCMP Capital, also held talks with Poundworld owner Chris Edwards but decided not to pursue a deal.
Former Asda chief executive Andy Bond is also thought to be interested in acquiring the chain as he prepares to launch fashion retailer Pep & Co this year.
Poundworld operates more than 270 stores and struck a £26m financing deal with Santander UK last year to support its expansion plans.
TPG bought a controlling stake in Victoria Plumb last year and was also part of the consortium that took Debenhams private in 2003, before re-floating it on the stock market three years later.
PricewaterhouseCoopers is understood to be advising on the sale.