Deutsche Bank, one of Germany's "big three" banks, is conducting a strategic review of DMG, its London-based investment banking arm.
The German bank, which is evaluating proposals to merge DMG with its commercial banking division, is expected to announce the results of its review "within weeks".
Under plans being evaluated by the Deutsche board, the name Morgan Grenfell, one of the oldest names in the City, could disappear.
A management reshuffle is another likely consequence of the proposed restructure. Michael Dobson, DMG's chief executive, is one of the Deutsche board members tipped as likely to change roles.
Mr Dobson could head up Deutsche's asset management division after the restructure. His post is likely to be filled by one of Deutsche's existing board members.
Morgan Grenfell, the UK bank bought by Deutsche in 1990, was initially run as a stand-alone operation. Three years ago, Deutsche merged its investment banking activities with those of Morgan Grenfell to create DMG.
"This [the proposal under consideration at Deutsche] is all the next step in the evolutionary process at Deutsche Morgan Grenfell," one industry commentator said.
DMG has expanded rapidly in recent years. Most of the growth has been organic - DMG has become notorious in the City for tempting employees away from rival banks with high salaries. But DMG has also made acquisitions, including the purchase last year of the equity derivatives unit of NatWest, the UK bank.
The key benefit of the restructure would be the potential for exploiting synergies between Deutsche's investment and commercial banking activities.
"It's all an issue of cross-selling products," commented Piers Brown, European banking analyst at UBS, who predicts Deutsche will attempt to sell investment banking services to its extensive commercial banking client base.
But Deutsche's proposals are far from risk free, according to industry experts. On the cultural side, the City predicts difficulties in integrating the more bureaucratic, traditionally less well-paid, commercial bankers, with their more colourful, highly paid investment banking counterparts.
Deutsche's commercial division has also spent many years building up its client base, at a substantial cost. If poorly structured, DMG could earn substantial profits from commercial bank customers at little incremental cost, which could fuel resentment within the bank.