The bank bosses are said to have delivered the warning at a round-table with the Prime Minister and a host of key US investors in New York this week. It included major City names such as Goldman Sachs, Morgan Stanley and BlackRock.
The Telegraph reported that the firms feel unable to wait for the final outcome of the two-year Article 50 negotiations before they make key investment decisions which could result in thousands of UK jobs being moved to Europe.
It added that Theresa May did not provide information about how the UK government would go about the Brexit negotiations, other than pushing for a deal which was "in the national interest".
"The message was clear from at least some of those present: if Theresa May cannot provide some early clarity about where the negotiations will end up, the only way to avoid that uncertainty would be a move towards Europe – there will not be time to wait," a source told the Telegraph.
Ahead of the UK's referendum on 23 June banks such as Citi and JP Morgan threatened to cut jobs if the Leave camp won. Citi and JP Morgan employ 9,000 and 16,000 people in Britain respectively.
The issue of financial services firms' much cherished passporting rights — the system that allows UK-regulated banks to operate across the European Union — are expected to be a prominent feature in the Brexit negotiations.