Suitors including private equity firms Advent, Apax, BC Partners, Cinven and PAI are expected to hand in tentative bids worth around 1.5 billion euros (£1.32 billion) by a pre-Easter deadline, they added.
Providence and the potential bidders declined to comment.
The auction is being run in parallel with preparations for a potential stock market listing before the summer, the sources said, adding that Providence will choose the path promising a higher valuation.
HSE24 is expected to post earnings before interest, tax, depreciation and amortisation (EBITDA) of 140 million euros this year and may be valued at 11-12 times that, the sources said.
Founded in 1995, HSE24 competes with companies such as QVC, part of John Malone's Liberty Interactive
Liberty Interactive has already been an active consolidator and in July bought the remaining 62 percent of peer HSN (>> HSN, Inc.) it did not already own in a deal that values the TV shopping network at $2.1 billion.
An 85 percent stake in HSE - which markets more than 20,000 different products to customers each year in Germany, Austria, Switzerland, Italy and Russia and in 2016 posted sales of 754 million euros - was sold to Providence for 650 million euros in 2012.
(Reporting by Arno Schuetze; Editing by Adrian Croft)