Sources close to the negotiations said talks between Deutsche of Germany and Bankers Trust of the US were well advanced, and that an announcement could be made as early as this week.
One source said: "You can take it that the reports are true. There may be an announcement very soon. You can't keep an orderly market in the shares of both banks if speculation is running riot."
Shares in both Bankers Trust and Deutsche soared on Friday as speculation mounted that the two were close to announcing a deal.
Deutsche - which has been actively seeking a US partner for some months - is thought to have offered between $7.5bn and $8bn for Bankers Trust, which has recently suffered heavy financial losses. The price represents a small premium over Bankers' current market capitalisation of $7.36bn.
The deal would be the largest ever foreign takeover of a US bank. It would add substantially to Deutsche's global custody and asset management businesses, although it would fail to propel Deutsche into the top 10 US investment banks, leading some analysts to criticise the deal.
One analyst said: "There will be an overlap in bonds and equities, where both are quite strong. However, it will not give Deutsche the strong corporate advisory franchise that it needs."
Other analysts were more positive about the deal, which would make Deutsche the world's fourth largest money manager.
The link-up would also boost Bankers Trust's capital base, generally perceived as weak. The bank, which recently reported third-quarter losses of $488m, is concerned that it will be unable to weather current volatile market conditions alone.
Employees at the investment banking divisions of both companies were said to be alarmed at the prospect of job cuts at a time when virtually all investment banks are cutting back on recruitment.
Senior executives at BT Alex.Brown, Bankers' brokerage house, are thought to be trying to force a partial sale of the investment banking division in an attempt to avoid the "jobs bloodbath" that followed the merger between Swiss banking giants UBS and SBC.
If the deal goes through, job losses are likely to be particularly heavy in the City, where both banks have extensive operations.
Many of BT Alex.Brown's London employees came to the US bank only a year ago from NatWest Markets, the former investment banking division of NatWest, and are said to be perturbed by the prospect of moving employer again so soon.
Ironically, Deutsche was at the time in the running to buy NatWest's equity division, but concerns over price and potential job losses are thought to have led NatWest to plump for Bankers Trust instead. The German bank eventually ended up with NatWest's smaller equity derivatives division.
Deutsche, whose chief executive is Rolf Breuer, has been actively looking for a US partner for at least four months, after more than 200 top bankers - including a top-rated high-technology team - quit its US operations.
At the time, Mike Philipp, head of equities, told staff: "The franchise has to be replaced. If we don't do anything we're sitting here dead in the water."