MILAN (Reuters) - Italian bank rescue fund Atlante is in talks with Monte dei Paschi di Siena (>> Banca Monte dei Paschi di Siena SpA) over a deal to help the country's third-largest bank to reduce its bad debts, two sources familiar with the matter said on Wednesday.

European Central Bank supervisors have told the Tuscan bank to cut its net bad loans by 40 percent in two-and-a-half years. That entails gross bad loan disposals worth nearly 14 billion euros (£11.7 billion) over the period, compared with a 5.5 billion euro target in the bank's current strategic plan.

A 360 billion euro pile of bad debts has become the focus of investor concerns over Italian banks, weighing heavily on their shares.

Monte dei Paschi, whose stock has lost 70 percent this year, has said it is working with authorities to solve its bad loan problem.

The bank wants to reach a deal by the end of July, when the results of European banking stress tests will be unveiled which Monte dei Paschi is expected to partly fail.

Shares in the bank soared as much as 15 percent on Wednesday as investors bet on a deal after press reports that it was close to hiring J.P. Morgan as an adviser for a large bad loan sale.

The two sources confirmed discussions between the Italian bank and Atlante were ongoing.

"They're constantly in touch trying to clinch an accord," one source said.

Monte dei Paschi, Atlante and JP Morgan declined to comment.

The gap between the book value of bad loans and the price investors are willing to pay has held back bad loan sales in Italy, as banks are reluctant to sell at a loss.

The Atlante fund has been tasked with buying bad loans from the country's weakest lenders at higher prices than sought by speculative investors.

But 60 percent of the 4.25 billion euros Atlante raised from Italy's leading financial institutions have already been spent to rescue two regional banks.

It is now looking for fresh funds which one source said could be used solely to buy Monte dei Paschi's bad debts.

Contributions could come from Italian state lender Cassa Depositi e Prestiti as well as, indirectly, from the Treasury.

However, private-sector funds are key to avoid breaking European Union rules on state aid and the moderate returns targeted by Atlante make it of little appeal for investors specialising in distressed assets.

(Reporting by Valentina Za, additional reporting by Francesca Landini; Editing by Keith Weir)