BBC News reports that Barclays is "staying anchored in Great Britain" he told BBC business editor Simon Jack.
Some banks have warned that the Brexit vote may affect jobs.
But Staley said: "Right now we are not making any plans to pick up and move people from one location to another."
That said, Barclays "wants to be involved in the capital markets globally" and wants to "stay connected to the European capital markets".
The bank will aim to take on new employees if access to Europe is restricted by Brexit, he said.
"You might have to increase your presence in another location - that doesn't necessarily mean you have to decrease [at] your location here," Staley said.
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