Deutsche Bank could agree this week to a penalty with the U.S. Department of Justice for allegedly misleading investors when selling mortgage-backed securities, one person with direct knowledge of the matter said on Monday.

"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.

In September, news that Germany's flagship lender faced a penalty of up to $14 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.