Collective Brands Inc. is reducing the potential pool of suitors for all or part of its business as it moves to the second round of bidding, people familiar with the matter told Bloomberg News. The report indicated that the company, which owns Payless ShoeSource, Saucony, Sperry Top-Sider, Keds and Stride Rite, began notifying the 20 bidders from the first round whether they would move on to the next.

In August, Collective Brands said it had hired investment bank Perella Weinberg to explore a possible sale.

The second round will comprise about 10 parties, sources told Bloomberg. Some of the private-equity funds may team up with retailers or other strategic bidders to put in combined bids for the whole retailer, sources said. Bidders in the next round will receive management presentations and access to a “second data room,” they added. The company remains open to selling itself piecemeal, separating out the Payless chain or the Performance + Lifestyle Group, or as a whole, source said.

The company also owns Collective Licensing, which is the owner and/or license operator of Airwalk, Above The Rim, Clinch Gear, STRIKEFORCE, Sims, Lamar and LTD, World Snowboarding Championships and Hind.

The Bloomberg report didn't indicate which firms made it to the second round. Initial offers were said to come in from buyout firms TPG Capital and Leonard Green & Partners LP, as well as from vendors including Wolverine World Wide Inc., Columbia Sportswear Co. and Deckers Outdoor Corp.

Based on bids so far, Collective Brands could get at least $20 a share if the entire business is sold, one source told Bloomberg. A $20 bid  values the company at $1.2 billion. On Tuesday, Collective Brands closed at $18.24.. The stock has risen more than 70 percent since Aug. 23, the day before the company announced its review.

Following the exit of long-time chairman, president and CEO Matt Rubel in June, the company in August announced that its board would, together with management, conduct a review of strategic and financial alternatives to further enhance shareholder value. Working with its advisors, Perella Weinberg Partners and Kurt Salmon, the company said it would “explore a full range of alternatives for Collective Brands.”

The company continues its search for a new CEO.