In September, it was revealed the German banking giant was facing a penalty of $14bn (£11.3bn) for mis-selling mortgage-backed securities.
It has previously been reported the bank would likely be settling the claim before the inauguration of new President Donald Trump on 20 January.
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Now, Reuters has reported that a person close to the matter said an announcement on the penalty could be made as early as Wednesday, adding: "There is a good chance that the case will be off the table before Christmas."
The source also noted the bank was likely to pay less than the $14bn price tag initially asked for by the US authorities, but added the deal was not yet finalised and a last minute hiccup in negotiations could cause any announcement to be delayed.
Deutsche Bank declined to comment.
Shares in the bank were trading down three per cent at €17.77 at time of writing.
Just yesterday, it was revealed the lender was considering scrapping bonuses to cover the costs of the fine.
In the bank's third quarter results in October, chief executive John Cryan noted the ongoing negotiations over the fine had unfortunately "overshadowed" restructuring work he and his team had carried out to return the lender to financial health.
Deutsche Bank also turned a surprise profit of €278m in its third quarter results. Not only was this a significant improvement on the €6bn loss it revealed in the same period the year before, it also beat analyst expectations.