Home Secretary Amber Rudd said that would not be desirable, "but we don't rule it out."
Rudd told the BBC today that Britain would get the best deal it could from the EU, but it would be a "two-way negotiation."
The EU's Schengen zone which includes most nations in the bloc is considering an electronic travel authorization system similar to one the US uses for visitors from selected countries.
Visitors from outside the EU would have to apply online and pay a fee before traveling.