Warburg Pincus bought the single-price discounter this week from Advent International in a deal thought to worth £200m.
The source told The Grocer a float was a serious long-term possibility and that Warburg would see it as an "attractive option".
Poundland has 270 stores but would now step up its growth plans, CEO Jim McCarthy said, suggesting it could reach 800 in total.
"We can expand faster and employ more people," he said. "We can now open 60 or 70 new stores a year."