And in another potentially damaging blow to London's status as Europe's main financial center, UBS's Weber told the BBC in Davos that 1,000 staff working in businesses that would be hit by Britain losing its "passport" to sell financial services in Europe would be affected.
Theresa May insisted she valued the contribution that banks make to Britain's economy, even as they signaled they were packing their bags in response to Brexit.
Leading financial firms warned for months before Britain's June referendum on European Union membership that they would move jobs out of the country if there was a vote to leave but have set out few details since on how many will go or where to.
Mr Staley admitted to concerns about "transition periods" while Britain's exit from the European Union is negotiated, but said London will fend off attacks from Frankfurt and Paris.
Stuart Gulliver, boss of British banking group HSBC, confirmed the bank is on course to move 1,000 jobs from its London office to France, where it already has a full-service universal bank after buying up Credit Commercial de France in 2002.
But the U.S. investment bank played down reports that the bank may cut London staff in half to around 3,000, while organising transfers to NY and to a new subsidiary in Frankfurt.
Day 1 at Davos and global elite discuss "leadership"
It has become one of the world's largest gatherings of government and business leaders to discuss major worldwide issues. More than half a dozen senior Chinese government figures will be in Davos this week, far more than in past years.
"We continue to work through all possible implications of the Brexit vote".
"There remain numerous uncertainties as to what the [Brexit] negotiations will yield in terms of an operating framework for the banking industry. Now we are now slowing down that decision", Blankfein told Bloomberg TV in Davos. But an upbeat Mr Staley said London remained vital.
The company is considering moving as many as 1,000 employees including traders and compliance managers to Frankfurt as the firm shifts operations across the Continent and to NY, the newspaper said.
Banks and financial companies in London have been waiting for some clarity on whether the United Kingdom will keep financial "passporting rights", which allow them to trade freely across Europe after it leaves the EU.
Migration was also a going to be a problem, with British bankers making the move could be "difficult".
HSBC shares closed 1.8 percent up, against a 0.2 percent fall in the broader European banks index.