Under UK takeover rules, Steinhoff has until 13th July to announce a firm intention to bid for the retailer.
Shares in Poundland rose 2% yesterday, after having surged 24% on Monday following the takeover rumour. The retailer told its investors to take no action, as there was no certainty that an offer would be made.
Earlier this year, Steinhoff pulled out of a takeover battle for Home Retail Group.
Steinhoff International Holdings is worth $22bn (£16bn), while Poundland is valued at more than £500m.
In September 2015, the retailer took over rival 99p Stores, but has since seen a slowdown in sales. Annual pre-tax profits at the chain tumbled 83.7% to £5.9m, although sales rose 18.7% to £1.3bn. Stripping out the acquisition, profits fell 13.5% to £37.8m on sales up 9.3% to £1.2bn.
However, Jim McCarthy, the departing chief executive, said that adding its smaller rival’s stores to Poundland has strengthened the group.