If Advent decided against an IPO, then several strategic buyers would be ready to step in, said German magazine Manager Magazin.
The publication previously reported that Douglas’ perfume and cosmetics stores perform better than initially expected.
Advent invested in Douglas in December 2012 and currently holds a 96 per cent stake in the business.
Last month Advent exited PVC maker Vinnolit to Westlake Chemical Corp in a €490m deal.
The firm acquired from chemical multinationals Celanese and Wacker Chemie 14 years ago.
Meanwhile, Advent is reportedly preparing to launch its sixth Latin American fund.
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