The potential initial public offering (IPO) and transtasman sharemarket listing of Carter Holt, tipped by market sources to be scheduled for the middle of the year, is likely to be a much smaller transaction.
There is speculation the deal will value the Australasian building supplies firm at about $1 billion.
Still, it could be the biggest sharemarket listing New Zealand will see this year.
The Swiss deal appears to have been a good one for Hart, given he purchased Sig for 1.7 billion euro in 2007.
Goldman Sachs advised Reynolds - the packaging and consumer products division of Hart's Rank Group - on the sale, while Onex was advised by Barclays, Bank of America Merrill Lynch and JP Morgan.
Sig, one of the world's biggest manufacturers of carton packaging for food and beverages, had revenue of 1.7 billion in 2013 and roughly 5000 staff across 40 countries.
The company was founded in 1853 and its varied history includes manufacturing firearms and railway cars for Switzerland's military.
With its tendency for highly leveraged deals, Hart's empire came under pressure during the global financial crisis, which squeezed earnings and put the spotlight on debt.
Reuters reported last year that a successful sale of Sig would help Hart reduce a US$18 billion debt pile accumulated through several leveraged buy-outs.
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These included a US$6 billion purchase of Pactiv Corp, whose brands include Hefty rubbish bags, in 2010 and a US$4.5 billion acquisition of Graham Packaging the next year.
Hart began building his packaging empire in 2006 with his takeover of Carter Holt, adding Alcoa's packaging business the following year.
He later bought International Paper's beverage packaging unit, and then Sig.
Hart previously had interests in the food industry with Goodman Fielder and Australia's Burns Philp.
The Financial Times reported in September that Rank had hired investment banks to sell Reynolds' US-based packaging firms Evergreen and Closure Systems International.
Carter Holt's pulp, paper and packaging businesses were sold for about $1 billion to Japan's Oji Holdings and Innovation Network last April.
Reynolds Group reported a loss of US$300 million from revenue of US$11.7 billion in the 2014 calender year, according to its annual report filed with the United States Securities and Exchange Commission.
Hart's wealth was estimated at US$7 billion by Forbes last month.
Reynolds Group
• The packaging and consumer product's division of Graeme Hart's Rank Group.
• Businesses include Evergreen Packaging, Pactiv, Graham Packaging, Hefty and Presto.
• Reported a loss of US$300 million from revenue of US$11.7 billion in the 2014 calender year.