He said the idea of someone having to prove they're not spreading a disease "can be a sensible one" but added the government is "some way off finalising any plans for Covid certification in the UK".
On the government's roadmap back to normality, foreign trips are banned until 17 May at the earliest.
The prime minister of France, Jean Castex, said on Thursday "the epidemic is spreading fast, and it's spreading everywhere".French hospitals warned they will soon be forced to prioritize which patients to treat, the Daily Telegraph reported.
He said "the goal must be to have unrestricted travel to "green" destinations" and said current testing costs "may be a deterrent to many United Kingdom travellers", urging government to "ensure that testing is required only where the public health risk justifies it". From 1 May, this could be replaced with proof of vaccination.
What will I need to do to travel?
Here we set out what restrictions are being lifted and what people in England will be able to do.
All adults and children in England will be able to have routine coronavirus tests twice a week as a way to stamp out new outbreaks, the British government said on Monday as it prepared to announce the next steps in lifting the nation's months-long lockdown.
Vaccine passports to facilitate worldwide travel are very likely to be required in the future, the PM said, as other countries seek to ensure tourists do not bring disease with them. "We're likely to face a summer of further disruption as health situations fluctuate, so airlines and holiday companies should be upfront about the risks and the disruption their flexible booking policies do and don't cover".
The prime minister stressed that he does not want to "underestimate" the risk of travelers importing the virus into Britain.
In contrast to many European countries that are entering new lockdowns to tackle surging cases, Johnson has set out a staggered plan to ease restrictions in the coming months.
But he added: "It's disappointing that the opportunity has been missed to provide more certainty to reunite families separated by travel restrictions, to give sunseekers the confidence to book ahead for their summer getaway and to help businesses across the country that have had their exporting ambitions placed on hold by the pandemic. The business travel industry continues to be crippled by today's lack of movement".
But it has not made clear whether it will issue "virus passports" for global travel, an idea backed by many tourism-dependent countries and airlines but opposed by more than 70 UK MPs.
The i reports the next major step on the Government's road map can be taken after the four key tests for containing the virus were passed.
Britain plans to use a traffic-light risk system for countries once non-essential worldwide travel resumes, but the government said it was too early to say which countries could be given the green light that would only require coronavirus tests before and after travel. "This is our last resort".
He went on: "Government cannot keep kicking the can down the road as hundreds of thousands of jobs are at risk".