Bain Capital, Advent International, CVC Capital Partners, Clayton Dubilier & Rice and Ares Management have all made it through the first round of bidding according to Reuters, which said the buyout could value Yankee at $2bn.
Madison bought into the business in 2006 through a $1.7bn take-private deal, which included the assumption of about $300m in debt.
A $2bn valuation would mean Yankee was worth 10 times its $200m EBITDA according to people familiar with the matter who spoke with Reuters.
The 44-year-old business had a net income of $56.3m in fiscal 2012, up slightly from the $54.5m it registered the previous financial year.
The firm had originally targeted $10bn for its sixth buyout fund, which was launched in 2007 before the financial crisis took hold.
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