By Paola Arosio and Stefano Bernabei

MILAN/SIENA (Reuters) - The European Central Bank has approved a privately funded rescue of Italy's third-largest lender, Monte dei Paschi di Siena <BMPS.MI>, three sources said on Friday, staving off the risk that regulators would be forced to wind up its business.

Under the bailout plan to be unveiled later in the day, Monte dei Paschi, struggling under a mountain of bad debts and accumulated losses, will raise 5 billion euros ($5.58 billion) in new shares and sell off soured loans to ensure its stability.

The Tuscan lender has been racing against the clock to get the plan in place in time for the release of European stress test results, also due on Friday night. These are expected to show the 544-year-old bank needs major balance-sheet surgery.

The Italian government is keen to avoid having to inject public funds to recapitalize the bank. Under European rules, this would entail politically unpalatable losses for Monte dei Paschi's bond-holders and depositors above 100,000 euros.

The bailout plan, drafted by advisers JP Morgan <JPM.N> and Italy's Mediobanca <MDBI.MI>, was approved by the Monte dei Paschi board after it rejected a rival recapitalization proposal put forward by investment bank UBS<UBSG.S>, sources said.

So far six banks - Santander <SAN.MC>, Goldman Sachs <GS.N>, Citi <C.N>, Credit Suisse <CSGN.S>, Deutsche Bank <DBKGn.DE>, Bank of America <BAC.N> - in addition to the global coordinators JP Morgan and Mediobanca have given a preliminary commitment to underwriting the planned share sale, a source said.

The health of the lender poses a threat to the wider Italian banking system, the euro zone's fourth largest, to the savings of thousands of retail investors and also to the increasingly weak political standing of Prime Minister Matteo Renzi.

Renzi faces a constitutional reform referendum in the autumn on which he has wagered his job. Monte dei Paschi is based in Renzi's home region and has some 5 billion euros of junior bonds, a large chunk of them held by ordinary Italians.

The bailout plan also includes a clean-up of the bank's balance sheet through the spin-off and sale of 10 billion euros of net non-performing loans, several bankers said.

Under the plan, the 5 billion euro share issue, which would be Monte dei Paschi's third capital increase since 2014, will be launched at the end of this year if possible, or more likely in early 2017, one source said.

However, bankers and analysts say it will be tough for the bank to lure investors, having already burned through 8 billion euros of capital raisings in the past two and a half years.

Monte dei Paschi's shares have lost nearly 80 percent of their value so far this year, taking its market value to less than 900 million euros.

(Additional reporting by Valentina Za, writing by Silvia Aloisi; Editing by Elaine Hardcastle)