The pair have hired JP Morgan to advise on a full or partial sale this year, the Financial Times reported on Monday, citing people with knowledge of the matter.
Potential bidders could include US media group Time Warner, the report said.
KKR and Permira bought a majority stake in the business in 2006 from German Media Partners, which includes Bain Capital, Hellman and Friedman, Saban Capital and Providence Equity Partners as investors.
That deal valued the stake at about €3.1bn, and the entire operation at €5.9bn.
The move comes two months after KKR and Permira agreed to sell ProSiebenSat1’s Nordic arm to trade buyer Discovery for about €1.3bn, and also follows the sale of the Benelux operations for €1.2bn in April 2011.
Lavena also plans to propose converting its non-voting preference shares into common shares, which could then be sold on the stock exchange to help it exit the business.
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