Investment banks Nomura and Daiwa Capital Markets met UK City minister Simon Kirby and the international trade minister for financial services, Mark Garnier, in a meeting on 1 December, according to the Financial Times.
In a "frank" discussion, executives from the two financial institutions laid out their intentions to leave the UK if they do not receive clarity on the City's "passporting" rights, which give institutions access to trade in the single market.
Sir Gerry Grimstone, chairman of Standard Life, told the Financial Times: "I think you are going to get a steady drumbeat of these kind of announcements (about moving) over the next few month, as everyone in the City starts talking to regulators, applying for licences, setting up subsidiaries and even taking options on buildings in the EU."
The revelation comes after it emerged that Lloyd's of London will set out its plans to leave the City next year. The insurance giant is choosing a destination from a shortlist of five countries that include Dublin, Paris and Frankfurt.
A Lloyd's spokesperson said: “Following the referendum we committed to looking at the options that would allow the Lloyd’s market to continue trading seamlessly with the EU.
"This included establishing a subsidiary model amongst others. We will continue to develop our plans on creating a subsidiary and will provide a detailed update to the market on the progress we have made early next year."