Cinven is expected to appoint an investment bank to advise on options on selling Gondola Holdings, which owns the Zizzi, Ask and Pizza Express chains.
Cinven bought Gondola Holdings for €1.3 billion (£1.1bn) in 2006, a year after it listed on the stock exchange for a second time. The group operates around 415 Pizza Express outlets in the UK and 50 overseas.
Gondola made £38 million profit before interest and taxation on sales of £592m in the year to July 2012. In Gondola's interim report chairman Chris Woodhouse said the group had delivered a resilient performance in the first half of the current year against a challenging backdrop. He said: "We do not anticipate any improvement in economic conditions in the near future."
Gondola sold the Byron burger chain for £100m earlier this month to the Hutton Collins private equity business.