ROME (Reuters) - Italy is in talks with European authorities over a possible 5-billion euro (4.24 billion pounds) state bailout of two Veneto-based regional lenders, two sources close to the matter said on Tuesday.

One of the sources said the discussions were at an embryonic stage and the final, combined capital shortfall of the two banks - Banca Popolare di Vicenza and Veneto Banca - had not been decided yet.

The sources said the scheme being discussed would be a precautionary recapitalisation of the two banks, which allows eurozone states to inject taxpayer money into lenders without violating state aid rules.

The Rome government has already won approval from the European Commission to use the mechanism for an 8.8 billion euro ($9.30 billion) bailout of Monte dei Paschi di Siena BMPS.MI, the world's oldest bank.

The two Veneto banks are owned by privately backed bank bailout fund Atlante, which rescued them last year after their attempt to raise money on the market failed.

The European Commission, the European Central Bank, Popolare di Vicenza and Veneto Banca declined to comment. The Financial Times first reported that Rome was looking at a possible precautionary recapitalisation of the two banks for 5 billion euros.

The Italian government last year earmarked 20 billion euros to help struggling banks.

The state is expected to provide 6.6 billion euros of the funds needed by Monte dei Paschi, raising questions over whether the 20 billion euros will be enough to bolster a banking industry weighed down by 356 billion euros of problematic loans accumulated during a harsh recession.

The two Veneto banks are studying a merger, which the head of Atlante said this month could be completed by early September. The fund has already pumped 3.5 billion euros into the two loss-making banks, but they need more capital to cover losses from expected fresh loan writedowns.

($1 = 0.9460 euros)