The divestment of Postbank, which has 1,100 branches and was bought for €6bn in stages from 2008, would be biggest strategic step yet for Deutsche under co-chief executives Anshu Jain and Jürgen Fitschen.
Under the first scenario being considered by the management board, Deutsche would sell shares in Postbank, 6 per cent of which remains listed, within the next 18 months and refocus its remaining own-brand retail business on more affluent clients.
At the same time, it would cut assets at its investment bank by €160bn – or roughly a fifth. The most likely areas of Deutsche's dominant investment bank to be reduced are the rates trading business and prime brokerage operation, which are both hit particularly hard by new Basel III capital rules.
Under the second more radical scenario being considered, Deutsche would split itself in to two separate legal entities. One would contain its investment banking, asset and wealth management and global transaction banking divisions. The second would contain all its retail businesses, which would be fully merged and then listed at some point over the next two and a half years.
Some analysts have said Deutsche should consider a complete spin-off of its retail banking unit to become a pure-play investment bank, like its US rival Goldman Sachs.
More from the Financial Times:
Deutsche Bank hit with $8.4m fine
HSBC speeds up exit from emerging markets
Deutsche Bank's Fitschen to stand trial
Joseph Dickerson, analyst at Jefferies, said in a recent note that Deutsche "should dispose of its retail unit," adding: "Deutsche is no Goldman Sachs, but the latter is a template."
A number of large Deutsche shareholders have previously told the FT that they are keen for the bank to retain a strong investment bank operation.
But many of them support the idea of it disposing of Postbank because it generates relatively low returns from its €144bn of mostly mortgage assets.
Retail banking in Germany is less profitable than in many other European countries because of fierce competition from the country's large number of local savings banks and Germans' traditional aversion to higher margin products, such as credit cards.
Deutsche's eight-man management board met last Wednesday, but has yet to decide formally in favour of either of the proposals, and various members have changed their positions over the course of the strategic review.
The bank's supervisory board is due to discuss the plans on Friday, but it is not yet clear whether the management board will be in a position to recommend one of the two options by then.
Unanswered questions remain over both. Spinning off the entire retail business would potentially provide Deutsche with a large enough slug of capital to avoid making deep cuts in its investment banking arm.
But it remains unclear whether Deutsche would still be able to meet tough regulatory requirements on funding in times of stress once it had been shorn of its retail deposit base.
Spinning off just Postbank is a lower risk option. But under this scenario, which would also include de-emphasising the rest of Deutsche's balance-sheet-intensive mortgage business, Deutsche would have to make deep cuts to its remaining domestic retail network of about 750 branches in order to keep its cost base in line with its lower retail revenues.
Deutsche said: "Strategy 2015+, our three-year plan launched in 2012 comes to its natural conclusion this year. We have been transparent that the bank is reviewing and updating its strategy, and that we will communicate further in the second quarter after decisions are made."