Advent International Apax Partners, Bain Capital and Cinven have all made offers for the company according to Reuters, which cited a source familiar with the matter.
3i hired Rothschild in October 2012 to explore sale options for Civica, which it bought in a £190m take-private deal in 2008.
The business provides software for UK councils, police forces and NHS trusts, and saw its revenues grow more than 40 per cent between 2007 and 2011 to £182.7m.
An earlier report by the FT said a stock market flotation in the first half of 2013 was also an option.
The planned exit is in line with 3i’s efforts to reduce its debt to under £1bn by June 2013 as part of an ambitious cost-cutting exercise led by new chief executive Simon Borrows.
Last month it made a 2.1-times return selling Canadian plastic equipment maker Mold Masters in a £615m deal, but also saw its £200m equity investment in Spanish business services company Enterprise wiped out when it exited its stake to Ferrovial.
The firm had more luck with its investment in UK restaurant chain Giraffe, selling its stake to Tesco last week for a 1.6-times money multiple.
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