MILAN (Reuters) - Shares in Italy's third biggest lender Monte dei Paschi di Siena (>> Banca Monte dei Paschi di Siena SpA) soared 20 percent in heavy volume on Wednesday, prompting speculation the bank's top investor may have found a buyer for part or all of its stake in the bank.

Three sources close to the situation and a financial source said the banking foundation that has just over 30 percent of the lender could have sold a stake. None of them however said they knew or were certain this had happened.

The foundation and the bank declined to comment.

Monte dei Paschi shares closed 19.2 percent higher at 0.22 euros, with around 1.5 billion shares changing hands - 10 times the average daily volume and around 12 percent of the bank's capital.

Italian watchdog Consob was probing the share performance in the troubled lender and has asked large trading houses in Italy and abroad for information on the price movements, a regulatory source told Reuters on Wednesday.

The foundation would have to inform Consob swiftly if it had sold down its stake.

"The shares started rising in afternoon trade when U.S. players came in," a banking source close to the matter said. "It is possible that the foundation sold a stake."

The financial source said: "The volumes today cannot just be due to short-covering. The hypothesis is that a big player has been buying and that this is linked to the foundation."

The Monte dei Paschi foundation, a not-for-profit entity with close ties to local politicians in the bank's home town of Siena, has been trying to find buyers for its stake in the lender for months to pay back creditors.

It is aiming to sell the bulk of its holding before a 3 billion euro capital increase the bank is due to launch in June, and time is running out. The foundation imposed a delay on the cash call to win more time to find investors.

Selling a stake would usually push down the stock price of a company.

But if the foundation finally found investors willing to take up a large stake in the bank and maybe even buy into the upcoming rights issue, that would boost Monte dei Paschi's shares by removing an element of uncertainty and possibly also fuelling takeover speculation, traders and bankers say.

A fifth source said one of the bank's private investors could have also sold a stake, without naming the investor.

The private investors in the bank behind the foundation are the Aleotti family, with 4 percent, French insurer Axa (>> AXA) with a 3.7 percent stake, and JPMorgan (>> JPMorgan Chase & Co.) with a 2.53 percent holding.

(Reporting by Elisa Anzolin, Gianluca Semeraro, Stefano Bernabei and Silvia Aloisi; additional reporting by Stephen Jewkes and Sophie Sassard in London, editing by David Evans)