The firm is currently in advanced takeover talks with the footwear group and a deal could be announced as soon as next month, said Sky News.
Dr Martens could sell for as much as £300m, said one of the sources.
The report said it is uncertain whether Permira will acquire the Dr Martens brand as insiders are suggesting that it will remain separate from the deal and the firm would be buying a licence to use it.
The private equity firm used to hold a stake in fashion group Valentino, which was sold to a Qatari investor in July 2012.
Permira picked up a controlling interest in Valentino Fashion Group for €5.3bn in 2007, but was forced to split off menswear brand Hugo Boss into a separate entity following the global financial crisis.
The firm is reportedly eyeing a January closing on the adjusted €5bn target for its latest fund, ahead of its original April deadline.
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