* Public money cannot cover additional loan losses
* Veneto banks expect to book fresh loan writedowns
* Other banks may have to step in if private capital needed (Adds government source, quotes)
MILAN, May 17 (Reuters) - Italy's healthier banks may have to once again step in to prop up two ailing Veneto-based regional lenders before taxpayer money can be used to rescue them, according to several sources familiar with the matter.
Popolare di Vicenza and Veneto Banca, two of the country's most troubled lenders, have requested state aid to help fill a capital shortfall of 6.4 billion euros ($7.1 billion) after loan writedowns pushed their capital below minimum thresholds.
They and fellow bailout candidate Monte dei Paschi di Siena , Italy's fourth-largest lender, present a crucial test of new EU rules for resolving banking crises, but negotiations over how to bail them out have been bogged down for months.
The rules, which came into full force last year, aim to limit the amount of public money that can be used to save weak lenders by imposing some losses on shareholders and bondholders.
Also, state aid cannot be used to cover incurred or foreseeable losses, such as those stemming from further writedowns on bad loans that the two lenders have already warned they will have to book this year.
The amount of those loan losses is not yet known, but the European Commission is insisting the two Veneto-based lenders plug the gap with private money, said six sources familiar with the matter.
With willing investors in short supply, other banks are likely to be the only viable source of private funds, they said, adding that this could be done through an existing industry fund set up to guarantee bank deposits.
"It's a problem because the state cannot cover the losses," an Italian government source said, declining to give precise figures.
Rome has set aside 20 billion euros to help its ailing banks, worried that if any of them failed that could destabilize the whole banking industry.
But while Monte dei Paschi, which must fill a capital gap of 8.8 billion euros, could have enough funds to cover loan losses that cannot be plugged by state money, the two Veneto banks are in a more precarious position, two of the sources said.
Both banks failed to raise funds on the market last year and had to be rescued by a hastily created, government-sponsored bailout fund financed by other lenders and financial institutions.
Now they may have no other choice than turning once again to healthier rivals for help.
Potential contributors are looking at this option with unease.
"We have already stumped up a lot money for the various funds that have been cobbled together to help weak banks," one of the sources said.
Both Popolare di Vicenza and the European Commission said negotiations were continuing.
Veneto Banca and Popolare di Vicenza, whose CEO Fabrizio Viola is leading talks with the European authorities, said they would not comment on what they described as rumors. They added discussions focused on targets set under a restructuring plan that envisages a merger between them.
Last year the two banks were rescued from bankruptcy by the industry bailout fund Atlante, which took up 2.5 billion euros worth of new shares that were spurned by investors. It later pumped another 938 million euros into the two banks, but one of the sources said it would not put in any more money.
Italian banks and insurers that funded Atlante have since been forced to write down the value of their investments.
The new rescue scheme under discussion for the Veneto banks entails a private contribution through the conversion of around 1 billion euros of junior debt into equity. The 938 million euros already paid by Atlante should also count as private capital.
But if, as expected, more money from private investors is needed, other banks would likely need to pay fresh cash into another fund that exists in other European countries and is meant to guarantee bank deposits for up to 100,000 euros.
In this case, to avoid breaching EU state aid rules, the fund has set up a separate, voluntary scheme which has already been used to rescue two small lenders in the past two years.
The fund's Director General Giuseppe Boccuzzi told Reuters on Wednesday that to date he was not aware of any such initiative. ($1 = 0.8980 euros) (Additional reporting by Andrea Mandala in Milan and Giuseppe Fonte in Rome; Writing by Valentina Za; Editing by Silvia Aloisi, Rachel Armstrong Greg Mahlich)