MILAN (Reuters) - Italy's third biggest bank, Monte dei Paschi di Siena (>> Banca Monte dei Paschi di Siena SpA), has asked the European Central Bank for more time to wrap up a 5 billion euro (£4.2 billion) rescue plan that was thrown into doubt by Prime Minister Matteo Renzi's defeat in a referendum at the weekend.

The bank, the world's oldest, has asked the ECB to give it until January 20 to do the deal, from a previous year-end deadline, it said in a statement on Wednesday.

The ECB could consider the request at a meeting of its supervisory board as early as Thursday. The meeting will discuss the situation at Monte dei Paschi, a source familiar with the matter said.

Renzi's bruising defeat in Sunday's referendum on constitutional reform has cast a pall over the bank's privately backed recapitalisation plan as investors are reluctant to commit money until the political situation becomes clear.

That has raised the prospect of a partial nationalisation of the bank, with sources telling Reuters on Tuesday that the Rome government could take a 2 billion euro controlling stake in the Tuscan lender.

Italy must come up with a solution quickly to avoid the crisis at Monte dei Paschi spreading to the wider banking sector, but the power vacuum created by Sunday's vote is not helping.

Renzi resigned on Wednesday, and a new government is expected to be appointed in coming days, but most parliamentary factions are pushing for an early election in a few months' time.

Monte dei Paschi needs to raise 5 billion euros to avoid being wound down, having been rated the weakest lender in European stress tests this summer.

It had planned to do so through a debt swap conversion that has raised just over 1 billion euros, a private placement with one or more anchor investors and a share sale that was due to start on Wednesday.

But the political upheaval following the referendum has all but dashed the bank's hopes to pull off the deal without state aid, bankers say.

Potential investors, including Qatar Investment Authority that had been considering injecting 1 billion euros or more in the lender, want to see what kind of government will succeed Renzi and whether early elections are on the cards before committing to back the deal, sources say.

As hopes that the private-backed cash call will succeed fade, the government is readying a decree that would allow it to pump 2 billion euros into the lender by buying subordinated bonds held by retail investors, two sources with knowledge of the matter told Reuters on Tuesday.

The government hopes an injection of state capital could help persuade private investors to stump up another 2 billion which, with 1 billion euros already available from a bond swap agreed with institutional names, would fill the 5 billion euros capital shortfall.

According to one person familiar with the matter, investment banks that must decide whether to go ahead with the private rescue deal, orchestrated by JPMorgan (>> JPMorgan Chase & Co.) and Mediobanca (>> Mediobanca Group), will make up their mind by Friday.

A source close to a U.S. private equity fund said on Wednesday it would be interested in putting money in the lender if the Italian government also injected cash and offered some guarantees for its investment.

"Now that the Italian state seems to be getting involved and the amount to be raised (on the market) is much smaller, there might be a good deal for us," the source said, adding however that certain conditions still needed to be met.

The government is already the bank's single largest shareholder with a 4 percent share.

(additional reporting by Francesco Canepa in Frankfurt and Pamela Barbaglia in London, writing by Stephen Jewkes; Editing by Adrian Croft)

By Silvia Aloisi and Stephen Jewkes