But following her speech on Tuesday setting out her Brexit strategy, which includes a full departure from the European Union's single market, bankers have begun setting out their own exit plans - from London.
Swiss bank UBS is also expected to shift jobs to the continent.
Goldman Sachs (NYSE:GS) is reportedly reconsidering plans relocate to London, amidst continued Brexit uncertainty.
On Tuesday, UK Prime Minister Theresa May confirmed that the United Kingdom would not remain a member of the European Union single market following Brexit, but instead would pursue bilateral free trade agreements with the bloc's members.
While May insists that Britain will abandon the EU's common market, Khan said she should press still in Brexit negotiations for "privileged access" to the trading area and for London to have the ability to hire the right talent from overseas.
"I value financial services in the City of London, and I want to ensure that we can keep financial services in the City of London", the prime minister said in an interview with Bloomberg editor-in-chief John Micklethwait at the World Economic Forum in Davos, Switzerland, on Thursday.
Jamie Dimon, boss of JP Morgan, which has already warned that 4,000 United Kingdom jobs are at risk, said on Wednesday: "It looks like there will be more job movement than we hoped for".
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Back-office personnel would move to Warsaw and investment bankers who advise French and Spanish companies would move to those countries, Handelsblatt reported, while trading staff who develop new products would move to NY.
Mr Gulliver added HSBC had an advantage over other banks, as it already has a presence in Europe after buying Credit Commercial de France in 2002, which holds most of the passporting rights it needs to trade in Europe.
Financial firms have accepted that they will lose their "passporting" rights to freely sell services across the 28-nation bloc after Brexit, but want more time to adapt to whatever terms are agreed with the EU. May said she would try to negotiate some form of market access.
"I don't believe that the financial centre of Europe will leave the city of London".
Barclays' chief executive Jes Staley, meanwhile, confirmed the bank's commitment to Britain.
Goldman Sachs chief Lloyd Blankfein said NY is "already a bit of a gainer" from Brexit, as the bank eases up on previous plans to shift operations to Britain. UBS shares were down 2.1 percent.