Home secretary Amber Rudd said she could not "rule out" the introduction of a scheme which would force those from outside the EU to pay for visas, the Telegraph reports.
The plan, currently being considered by EU nations, emerged over the weekend.
Rudd said the UK could create a similar system in response if British citizens were hit with a charge.
The scheme, which could cost around £10pp, has been branded a "holiday tax" and critics have called on prime minister Theresa May to rule it out.
Asked about plans for a EU visa, Rudd said the British people would be "surprised" at being forced to pay.
She added: "I don’t think it’s particularly desirable but we don’t rule it out because we have to be allowed a free hand to get the best negotiation."
She said: "It’s a reminder that this is a two-way negotiation.
"The EU and the commissioners may be considering alternatives - they will be considering their negotiations with us, just as we are considering it with them."
The plans, which have been drawn up by the European Commission, are similar to the American Esta model where travellers pay $14 and apply online before they are allowed to enter the US.
It would mean anyone entering the 26-nation Schengen passport-free travel zone, of which the UK is not part, would have to pay for a visa waiver if their home nation is not part of the agreement.