In an interview with Mr Osborne at an event last year, the Coinbase boss claimed US officials were punishing the cryptocurrency industry and would not rule out moving to the UK in the future.
Mr Armstrong said: “The UK is our second largest market. We are not seeing regulatory clarity in the US. We may have to consider investing elsewhere. Anything is on the table, including relocating.”
He added that he would consider re-listing the business in London rather than New York, since the US had failed to bring in clear laws for cryptocurrency businesses.
Rishi Sunak has sought to woo cryptocurrency companies and claimed he wants to make Britain a “global crypto hub”. So far, however, UK regulators have failed to take a clear stance on cryptocurrency companies and several businesses have pulled out of Britain.
Other members of Coinbase’s advisory council include Mark Esper, the former US secretary of defence, as well as former US senators and congressmen.
Mr Osborne is one of several current and former Tories politicians who have taken up roles in the cryptocurrency industry, despite concerns over the role of digital currency in financial scams, ransomware, hacking and sanctions evasion.
Former chancellor Lord Hammond serves as an adviser to UK crypto company Copper, while Lord Vaizey, the former digital minister, is on the global advisory board of Binance.