An independent delegation headed by former city minister Mark Hoban will try to close a free-trade deal in Brussels, according to people familiar with the "unofficially supported" plan.
A number of banks have set up contingency plans after Theresa May said that with Brexit the United Kingdom would leave the single market.
Some banks have announced plans to move staff, while others have stepped up operations at European Union sites in cities including Frankfurt and Dublin.
Financial services firms now based in the United Kingdom will face €15bn of restructuring expenses and up to €40bn of extra tier one capital requirements, according to research for the Association of Financial Markets in Europe.
It is believed the free-trade plan will make a credible blueprint for the Brexit negotiations amid fears of a hard or no-deal Brexit.
City leaders are nervous that the March 2019 deadline for the UK's departure from the European Union (EU), will badly hit Britain's status as a European financial centre unless it secures an additional deal.
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Mr Davis is due to host a conference for business leaders at Chevening House in Kent on Friday as part of a Government drive to give them a bigger say in the Brexit process.
Instead officials are said to be warning that there will have to be a "binary" choice between a deal similar to the European Economic Area (EEA) or a more limited free trade arrangement similar to that struck between the EU and Canada.
Mrs May's strategy, set out in her Lancaster House speech in January, is to leave the single market and customs union to gain full control of immigration, but still strike a "comprehensive" free trade deal with cross-border commerce to be "as frictionless as possible".
Foreign Minister Boris Johnson had said that Britain "can have its cake and eat it".
Asked to respond to reports of ministers now being forced to consider a trade-off, he said they "did not recognise the language".
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