The digital retailer is expected to announce the deal for Ideal Shape in the coming days, Sky News reported.
Hut Group reported group sales of £334m, up 35 per cent year-on-year, and earnings before interest, taxation, depreciation and amortisation (Ebitda) of £30m, up 33 per cent, in 2015.
The company has also completed the acquisitions of Skinstore from the owner of Boots and Hale Country Club and Spa in recent months.
Ideal Shape was founded in 2003, has a focus on female consumers and is growing revenues by more than 250 per cent annually.
Hut Group is chaired by Co-Operative Group chief executive Richard Pennycook and counts former Tesco boss Sir Terry Leahy and Ocado chairman Lord Rose among its investors.
Hut Group has been asked for comment.