The UK should scrap home and hotel quarantine for travellers coming from low-risk countries, Heathrow Airport chief executive John Holland-Kaye said.
The airport on Thursday proposed that the government should introduce a traffic-light system that assesses the risk of imported Covid-19 cases based on the passenger's country of origin.
The suggestion comes as a review of international travel is expected to be announced on Monday.
Under the government’s road map out of lockdown, international tourism is scheduled to resume on May 17, but this may be delayed given surging case numbers in Europe and the potential risk for new variants to enter the UK.
But Mr Holland-Kaye said quarantine requirements should be removed for passengers from countries with low levels of coronavirus.
"We need a new level in between the amber and the green [levels of risk], where you have low levels of variants of concern but still some issues and you might have to have testing before you get on the plane, possibly testing after you've arrived, but no need for quarantine," he told the BBC.
"And that's the big change we need to see: stepping away from quarantine as the main control."
He said the airport was pressuring the government to reach a point “where we can travel as we used to”. Countries with high inoculation rates, such as Israel and the US, should be at the front of the queue.
“It may be several months away but we’ve got to start planning now,” he told Sky News.
“Some will open up faster than others. You can imagine that would happen in countries such as Israel where they have very high vaccination levels, very low Covid levels and good controls.
“They might open up earlier than countries such as Germany and France, where the opposite is the case.”
Paul Charles, from The PC Agency travel consultancy, said several countries could be added to a future “green list”.
Citing data from the European Centre for Disease Prevention and Control, he included the UAE on the list of countries the government should consider allowing travel to and from.