The company, which operates under its Mehiläinen and Carema brands, could fetch somewhere in the €700m (£611.9m) to €1bn range, the bankers said, higher than last year’s estimate of around €600m to €700m.
Ambea, which provides specialist healthcare in nursing homes and for disabled people, generates stable cash flows.
However, with operations in Sweden, Finland and Norway it could present a multi-jurisdiction challenge for a private equity buyer, according to one of the bankers.
The group generated earnings before interest, tax, depreciation and amortisation of roughly €70m in 2009, several bankers said.
Ambea said 2008 EBITDA was 658.3m Swedish crowns , while net debt stood at 2.8bn Swedish crowns.
Other privately-owned European companies have explored both a public listing and a sale, including UK pet shop chain Pets at Home, which KKR bought from Bridgepoint last week for £955m including debt.
3i explored a possible sale of Ambea earlier last year, but desisted as the credit crisis froze activity in the European leveraged buyout market, one banker said.
Possible bidders now include Advent International, BC Partners and Investor AB working alongside Goldman Sachs, according to two bankers.
Ambea is majority-owned by 3i and related funds, which hold 75 per cent of the company, while GIC owns 15.1 per cent and management owns the remaining 9.1 per cent.