By Tom Finn and Arno Schuetze

DOHA/FRANKFURT (Reuters) - Deutsche Bank has secured backing from its largest investor and is seeking advice from other banks as it scrambles to restore market confidence undermined by a demand by U.S. authorities for up to $14 billion over mis-selling allegations.

Qatari investors who own the largest stake in Germany's largest bank do not plan to sell their shares and could consider buying more if it decides to raise capital, sources familiar with Qatari investment policy told Reuters.

"Purchasing more (Deutsche Bank) stock - that could be considered ... which is not to say there are any imminent plans to do that," said a source close to the Qatari investors who own just below 10 percent in Deutsche Bank. The source declined to be identified as the matter is confidential.

If a capital hike does turn out to be required, the Qatari investors would probably take part in it as they want to keep their roughly 10 percent stake, a second source close to the matter added.

Deutsche shares plunged to record intra-day lows below 10 euros last week on Friday and although they have since rebounded to just above 12 euros, they are 13 percent below last month's peak and 46 percent below their close at the end of last year.

That implies the Qataris may have lost, on paper, over $1.2 billion on their investments in the bank.

German weekly Der Spiegel reported, without citing sources, that Qatari investors around Sheikh Hamad bin Jassim al-Thani, with backing from sovereign wealth funds, were mulling taking a 25 percent in the lender, sending Deutsche Bank's U.S.-listed shares higher.

But sources familiar with the situation told Reuters it was unlikely that the Qataris would acquire a stake as big as 25 percent.

Deutsche Bank declined to comment and Sheikh Hamad was not immediately available for comment.

HIGH LEVEL TALKS

Deutsche Bank CEO John Cryan, who is attending the International Monetary Fund and World Bank's autumn meetings in Washington, is due to meet with the Department of Justice as well as with senior managers of other investment banks in the United States to discuss the lender's options, people familiar with his schedule said.

However, the talks with other bankers are expected to focus on immediate steps the German bank may be able to take such as asset sales, rather than asking shareholders for fresh cash.

"The cap hike issue will unlikely be the focus of most of those meetings," one of those people said, adding that pulling off a capital-raising would be a well-rehearsed exercise which does not need too much advance discussion.

Deutsche Bank declined to comment on Cryan's discussions.

Separately, German Economy Minister Sigmar Gabriel said that while Deutsche Bank faced enormous challenges with potential fines in the United States, moves by its leadership to change the bank's business model showed it was reacting to the risks.

Gabriel said the government did not have its own risk assessment for the bank, but that Germany was keen to see the 146-year-old bank succeed in the longer term.

"It's completely obvious that we have an interest in Deutsche Bank again becoming a stable financial institution that is successful nationally and internationally," Gabriel said. Germany's largest bank is under heavy pressure as it fights the penalty that the U.S. Department of Justice (DOJ) plans to impose for mis-stating the risks of securities the bank sold ahead of the 2008-2009 financial crisis. This sent its shares to a record low last week and spooked clients.

Deutsche Bank's proposed fine has emerged as another bone of contention between the United States and the European Union after the EU said earlier this year that U.S. tech giant Apple Inc owed $14 billion in taxes. The chairman of euro zone finance ministers, Jeroen Dijsselbloem, told Reuters that the fine was disproportionate and could place Europe's financial system at risk.

"Here is a financial institution which needs to be restructured and strengthened and needs to bring in new capital and we cannot then have an even bigger amount of capital being pulled out by the American authorities. That is really counterproductive, to put it mildly," he said.

SMALLER FINE IN STORE

Deutsche says it expects to settle with the DOJ for far less than $14 billion, in line with other big banks that negotiated over similar allegations.

IMF chief Christine Lagarde gave it some tough advice on Thursday, saying it needed to reform its business model and rapidly reach a deal with U.S. regulators.

Deutsche is cutting back a workforce of around 100,000, revamping information technology and shrinking non-core assets. Unlike some European peers, it is sticking with investment banking, with a global reach that the IMF says makes it among the riskiest of all banks.

CAP HIKE

Launching a capital increase before a settlement with U.S. authorities is seen as unlikely as few investors will be willing to buy shares without being able to gauge the impact on the lender's capital, equity capital markets bankers said.

"And even when a settlement is eventually reached, Deutsche Bank is likely to wait for its share price to recover before launching a cap hike. Currently it would only be able to raise 4.5-5 billion euros and they may want more," one banker said.

"A cap hike could be done in the first half of 2017 at the earliest," another banker said. Deutsche Bank ranked 7th worldwide in global equity capital markets according to Thomson Reuters data. While it has the in-house expertise for a capital increase it will rely on other investment banks. In 2014, 25 helped with its rights issue.

"At this stage, no bank has gotten any mandate for a cap hike," a person close to Deutsche Bank said.

Most banks will be called in just days before any deal, which will likely be structured as a fully underwritten rights issue with banks guaranteeing to take on shares to sell on to a mix of investment funds, pension funds and hedge funds.

Meanwhile, some of Germany's top industrial companies have revived a decades-old network to discuss taking a direct stake in the bank as a way to help shield it, one executive at a large DAX-listed company has said.

(Additional reporting by Katrhin Jones, Alexander Hübner, Pamela Barbaglia, Sophie Sassard, Joseph Nasr, Andrea Shalal and Jan Strupczewski; Editing by Jonathan Oatis and Alexander Smith)