FRANKFURT/NEW YORK (Reuters) - Deutsche Bank  (>> Deutsche Bank AG) could this week agree a penalty with the U.S. Department of Justice over the sale of toxic mortgage debt, one person with direct knowledge of the matter said on Monday.

The penalty stems from a 2012 initiative launched by U.S. President Barack Obama, a Democrat, to penalise banks for allegedly selling sub-prime debt while misleading investors about the risks, a practice that contributed to the worst economic crisis since the 1930s.

"There is a good chance that the case will be off the table before Christmas," the person said, adding that an announcement could come as early as Wednesday.

This would remove the biggest uncertainty facing the bank, which had sought a deal before President-elect Donald Trump, a Republican, takes office on Jan 20.

In September, news that Germany's flagship lender faced a penalty of up to $14 billion (£11.26 billion) caused Deutsche's shares to plunge and later prompted the bank to deny speculation that it needed a bailout from Germany.

Any last-minute hitch in negotiations could delay an announcement and the person cautioned that a deal was not yet finalised. A spokesman for the Department of Justice declined to comment.

Deutsche Bank, which used to be a major player in the U.S. mortgage market, is set to pay far less than the $14 billion penalty the U.S. authorities had initially asked for, the source indicated. Deutsche Bank declined to comment.

Deutsche Bank was one of the most high profile European banks involved. It had a 6.4 percent share of the retail mortgage backed securities market, according to rating agency Moody's.

That was slightly less than Goldman Sachs, which reached a settlement earlier this year of roughly $5 billion.

Record settlements have also been reached with U.S. banks such as Bank of America (>> Bank of America Corp).

Now the focus has turned to Europe's Deutsche Bank (>> Deutsche Bank AG) Royal Bank of Scotland (>> Royal Bank of Scotland Group plc), Credit Suisse (>> Credit Suisse Group AG), Barclays (>> Barclays PLC), UBS (>> UBS Group AG) and HSBC (>> HSBC Holdings plc).

(Writing by Arno Schuetze; Editing by John O'Donnell and Keith Weir)

By Andreas Kröner and Karen Freifeld