Speaking with Sky News, the deputy governor was asked about the BoE's stance on cryptocurrency in the wake of the FTX collapse in the US.
The cryptocurrency exchange filed for bankruptcy on 11 November, with its valuation falling from $32bn to insolvency in a matter of days, causing the crypto market to lose billions in value amid the volatility.
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In the interview, Cunliffe said the trading of crypto assets had not been sizeable enough to destabilise the financial system, "but it was starting to develop links".
He added: "I do not know how that would [have] developed, but we had banks and investment funds and others who wanted to invest in it."
Commenting on the BoE's future plans to manage the asset, Cunliffe said: "We should think about regulation before it becomes integrated within the financial system and before we could have a potential systemic problem."
Cunliffe said that while crypto trading "is not something I would do" he said that for people who do want to enter that space, there should be "consumer protection and market integrity" akin to that provided for "similar activities".
The central bank itself has been making some moves in this space, as it is currently seeking out third-party supplier to develop a mobile wallet for a central bank digital currency (CBDC).