The company said it was considering giving UK shops incentives to only accept debit and credit card payments after introducing the concept in the US.
Visa has struck a deal with about 50 US businesses to receive US$10,000 if they refuse coins and notes.
Consumer groups have criticised the scheme, saying that cash remains a critical part of society.
"It is easy to categorise it as a bribe, but ultimately they are incentivising companies to do away with cash, and that's not the job of people like Visa," said James Daley of consumer group Fairer Finance.
Despite the incentive, retailers may be put off by such a deal as they have to pay fees on card purchases. On average, companies pay 16p on each credit card transaction and 5.5p on each debit card payment.
UK retailers paid £800mln on interchange charges last year.
Visa said in a statement that it that after bringing the incentive to US companies, it hopes to bring “similar cashless initiatives to other countries, including the UK".
"At this time, we do not have a firm plan on when such an initiative would be available in the UK."
Visa chief executive Al Kelly told investors in June that the company was "focused on putting cash out of business".
"The number one growth lever [for the company] is the conversion of cheque and cash to digital and electronic payments."