The Transport Secretary says he is "very hopeful" a new testing regime for travellers to the UK can be in place by 1 December, reducing the amount of time people need to spend in quarantine.
Grant Shapps said it could happen as long as there was enough testing capacity to support the plan.
The government has been consulting on a system where passengers would be tested after just a week of isolation.
But BA's new boss wants testing before departure, not quarantine on arrival.
Addressing an online aviation conference, Mr Shapps said the government was looking at introducing a virus test alongside a shortened quarantine period by early December.
"My ministerial colleagues and I have agreed a regime, based on a single test provided by the private sector and at the cost to the passenger, after a period of self-isolation," he said.
"It will mean a single test for international arrivals, a week after arrival."
The government's travel taskforce, which is working on the plans, will put its recommendations before the prime minister in November, Mr Shapps said.
The idea is to reduce the amount of time travellers coming into the UK have to spend self-isolating - currently 14 days for those arriving from areas not included on the government's list of "travel corridors".
The government's approach may be designed to protect public health, but is unlikely to win it many friends in the aviation industry.
Just before Grant Shapps spoke, and at the same event, British Airways' new boss Sean Doyle used his first major public appearance since his appointment to argue for a "fundamental rethink" of the UK's approach to flying during the pandemic.
It was time, he said, to replace the current quarantine regime with a "reliable and affordable" test taken before flying.
People within the sector blame the current restrictions for killing off hopes of a strong revival in the sector, after the lockdown earlier this year.
The prospect of spending two weeks in isolation, they say, is simply deterring people from travelling. Ryanair plans to operate at 40% of its normal capacity this winter, while Easyjet will have just 25% capacity.
Mr Doyle suggested that even a reduction in the quarantine period to seven days would not be enough to change matters.
But Mr Shapps made it clear the government will press on with its own plans.
Speaking at the same conference, British Airways' new boss Sean Doyle emphasised his objections to the current system.
"We need to get the economy moving again and this just isn't possible when you're asking people to quarantine for 14 days," said Mr Doyle, a week after he replaced Alex Cruz as chief executive of the airline.
However, he said that even if quarantine was reduced to seven days, demand for travel would remain low, and called for tests before departure.
"People won't travel here and the UK will get left behind," Mr Doyle said.
Mr Shapps said the government was in talks with the US about trialling pre-departure tests, but no agreement has been reached yet.
British Airways is currently slashing thousands of jobs amid a slump in demand for air travel - a pattern seen at other carriers.
Some warn there could be hundreds of thousands more cuts unless the sector gets additional government support.
The International Air Transport Association has downgraded its 2020 traffic forecasts, after "a dismal end to the summer travel season".
The association, which represents 290 airlines, estimates that it will be at least 2024 before air traffic reaches pre-pandemic levels.