In other words, they want her to delay triggering Article 50, and therefore a Brexit, for as long as possible.
The Financial Times reports that at a meeting in New York earlier this week banks asked for a "long lead time" of up to two years to prepare for Brexit and a period of transition for them to adjust to the new world.
May told National Public Radio in the US, as per The Sun, that: "One of the purposes of my meeting with US investors, and that included US banks, was to hear from them what their concerns are and what their key issues are as we go forward with our negotiations.
"I hope the message they took was that I recognise the importance of financial services and the City of London as an important international financial centre."
May also signalled in that interview that Article 50, which officially begins the process of Britain leaving the European Union, would be triggered by a letter.
Once Article 50 is triggered, Britain will have a two-year window to negotiate its exit. It is unclear if this will satisfy the bank's calls for a "long runway" to prepare.
Financial institutions are concerned Britain will lose its passporting rights, which allow them to operate across the European Union using a single British licence.
The EU has said that Britain must accept free movement of people if it wants to keep passporting rights but Theresa May has signalled she is determined to curb migration, saying as much to Wall Street chiefs according to the FT.
The European Union is signalling it won't cut a special deal with the City of London if the UK leaves the European single market and banks such as JPMorgan and UBS have already warned of potential post-Brexit job losses. Deutsche Bank has also prepared a secret briefing paper looking at where banks may want to relocated to, obtained by Business Insider.
The Financial Conduct Authority revealed earlier this week that 5,500 companies in Britain with a collective revenue of £9 billion ($11.7 billion) that benefit from passporting rights.