* Italy seeking to salvage two ailing regional banks
* Banco Popular's overnight rescue steps up pressure
* Lack of private investors hinders Italian rescue (Recasts with comments)
MILAN/ROME, June 8 (Reuters) - Italy's biggest banks may help Rome bail out Popolare di Vicenza and Veneto Banca to avoid being hit by costly depositor guarantees if European regulators shut them down, sources close to the matter said on Thursday.
Wednesday's overnight rescue of Spain's Banco Popular by Banco Santander has increased pressure on Italy, which has been trying to win European Union approval for its planned bailout of the two regional banks for months.
Rome has so far failed to find investors ready to put in the 1.2 billion euros ($1.35 billion) in private capital that EU authorities are demanding to authorise the plan.
The "resolution" of Banco Popular could strengthen the case for winding down the two Veneto banks, an EU official said on Wednesday.
Italian banks would have to shell out 11 billion euros to protect depositors at Veneto Banca and Popolare di Vicenza if the two banks were wound down, one source said on Thursday.
Under Italian law, deposits up to 100,000 euros each are guaranteed by a depositors' protection fund which is financed by healthy lenders and would have to be replenished if the two Veneto-based banks were shut down.
The source said Italy's healthier banks and the government were looking at a plan under which each lender would contribute to provide the 1.2 billion euros required based on the size of their deposits.
Some leading banks were already agreeable, but only if others signed up.
A second source said Rome was putting pressure on heavyweights Intesa SanPaolo and UniCredit to take part so that other banks would follow their example.
UniCredit CEO Jean Pierre Mustier has held talks with the Rome government and European authorities, the first source said.
The two Veneto-based banks, weighed down by bad debts and mounting losses over the past three years, need a total of 6.4 billion euros in capital. One possible vehicle for private investment would be an existing bank rescue fund.
Unlike Spain or Ireland, Italy did not tap EU funds to repair its banks during the financial crisis and is now seeking to prop up its weakest lenders under strict new rules that aim to shield taxpayers by forcing losses on investors.
Rome won a preliminary green light from Brussels this month over its a proposed rescue of its fourth-largest bank Monte dei Paschi di Siena.
But drumming up support for the Veneto banks has proved a challenge as Italian banks already spent 3.4 billion euros last year to save them from bankruptcy.
Further loan losses and deposit flight have drained the two lenders of capital, forcing healthier rivals, which own them through state-sponsored bailout fund Atlante, to write down the value of their investment. ($1 = 0.8901 euros) (Writing by Valentina Za; editing by Jane Merriman and Alexander Smith)