CVC plans to raise 1.35bn Swiss francs (£864m) by selling shares in the company to slash the telecom giant’s debt pile.
The buyout giant, headquartered in London, bought Sunrise in 2010 for SFr3.3bn.
A listing could value the company, currently the country’s second biggest telecoms outfit behind Swisscom, at about SFr5bn.
It would be the biggest since defunct oil refiner Petroplus floated on the Swiss market in late 2006.
Deutsche Bank and UBS will run the offering, with help from Morgan Stanley and Berenberg running the order books. Vontobel is also co-lead manager on the offering.
CVC – an acronym of Citicorp Venture Capital, reflecting its background as a former arm of Citi – is one of Europe’s biggest private equity firms and has a host of portfolio companies.
Last year it floated Brit Insurance on the London stock market and in 2013 listed Merlin Entertainments on the same exchange.