Mr Staley, who has held the top job at the bank since 2015, said he believed Brexit had the potential to deliver a more "positive" future for Britain.
"I think Brexit is more than likely on the positive side than on the negative side," he said in an interview with the BBC.
While some jobs in the financial services sector that might have been created in the UK have moved to EU countries as a result of Brexit, Mr Staley said the situation was an opportunity for the UK and London to look beyond Europe.
"I think what London needs to be focused on is not Frankfurt or Paris – it needs to be focused on New York and Singapore," he said.
"Brexit gives the UK the opportunity to define its own agenda and in defining that agenda around financial services staying competitive with other markets outside of Europe is really what the government here should be focused on and I think that is what they're focusing on," he said.
Mr Staley also said that Britain needs to make sure London "is one of the best places, whether it was regulation or law or language, or talent that manages these flows of capital well".
While the Barclays boss advocated for competing with countries outside Europe to do that, he said he could not support widespread deregulation to achieve that goal.
"I wouldn't burn one piece of regulation," he said.
Rather, he suggested that the UK's strong regulation was a strength, rather than a weakness, with the Barclays boss praising a recent effort to crack down on firms offering "buy now, pay later" schemes.
"You see what's happening right now with 'buy now, pay later', you know... The FCA is going to come in and start to increase the regulation of that marketplace. That's the right thing to do," he said.
"And, in a funny way we've gotten pretty good at working inside the regulatory framework that is here. It protects the financial industry in London as we learn how to deal with this regulation, and it makes the bank safer," he said.
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