The company has an EBITDA of $90m could be valued at nearly $1bn in a deal, said Reuters, citing people familiar with the matter.
Odyssey has hired investment banks Barclays Plc and Harris Williams & Co to manage the sale.
The firm bought Ranpack from American Capital in Strategies in 2008 for $410m, according to data from law firm Weil, Gotshal & Manges, which advised on the deal.
Meanwhile, Odyssey is reportedly nearing another exit deal. It is said to be close to selling aircraft part manufacturer Wencor Group to fellow private equity firm Warburg Pincus.
According to Reuters, a deal for as much as $900m is close, after Warburg Pincus beat other private equity firms in an auction process.
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