Deutsche said: "The bank will review and update its strategy over the course of the coming year. It is irresponsible to speculate on the sale of any business."
A spin-off of Deutsche's retail business, which has 2,700 branches mostly in Germany, would also underline how big European banks are being forced to consider dismantling themselves to comply with new structural reforms.
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Germany is considering moves to bring its law on structural reform of banks more closely into line with European Union proposals to force lenders to separate their trading activities from their other operations.
Deutsche has been prevented by BaFin, its domestic regulator, from using the deposits of its retail customers to finance operations in its corporate and investment bank, the person said. BaFin declined to comment.
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The bank also faces pressure from regulators to boost its leverage ratio, a gauge of indebtedness that measures equity against total assets, which rose to 3.2 per cent after an €8bn share sale last year, but still lags behind many of its main rivals.
Selling the retail bank would boost its leverage ratio by removing a big mortgage portfolio from Deutsche's balance sheet.
Mr Jain and Mr Fitschen face growing pressure from investors to take radical action to reverse several years of disappointing performance.
Deutsche's shares, which have fallen more than 36 per cent in the past 12 months, dropped another 2 per cent on Wednesday. They have fallen more than a quarter since the duo outlined their first three-year strategic plan in September 2012 — against a 14 per cent rise in the MSCI world banks index.
Postbank is 94 per cent owned by Deutsche, but it still has a small free float that could make a share sale easier. Shares in the postal bank, which has a market capitalisation of €7.9bn, rose slightly after reports about a potential spin-off.
Analysts are predicting that Deutsche will be forced to abandon its return on equity and cost-income targets by the time they present their new strategic plan.
With a return on equity of 2.8 per cent in the third quarter, analysts say the bank's target of 12 per cent by 2016 seems out of reach, unless it is bailed out by a dramatic revival in the fixed income trading market.
Its private and business client division, which caters to 23m retail and small business customers, had an after-tax return on equity of only 6 per cent in the third quarter. The unit made €7bn of revenues and €1.1bn of pre-tax profit in the first nine months of 2014.
Deutsche's next strategic plan is likely to also feature further cutbacks in its investment bank and an expansion of its wealth and asset management unit, which is close to having €1tn under management for the first time.