People could be asked to check their temperature at home before they travel on public transport, under plans being looked at by the government.
The prime minister is due to reveal details next week of how the COVID-19 the lockdown will be eased, allowing more people to go to work and children to return to school.
Boris Johnson has been open about his keenness to boost the struggling economy but there are concerns that ending the lockdown too quickly could result in a second wave of infections and deaths.
One of the places of concern would be public transport, where trains and buses were often crowded during peak times before the virus outbreak.
The Times reported that commuters could have to take their temperatures before travelling and anyone with a high temperature – a COVID-19 symptom – would need to stay home.
Meanwhile, The Daily Telegraph reported that social distancing rules requiring people to stay two metres apart could be reviewed in the hope this would allow more businesses and schools to reopen.
The government said on Friday that it had passed its target of carrying out 100,000 coronavirus tests per day by the end of April.
But the numbers were boosted by around 27,000 tests sent to homes, which had not previously been counted in testing figures and are now counted as they are dispatched.
Health Secretary Matt Hancock has said that the next phase of dealing with the virus outbreak will be dominated by community testing and contact tracing.
He told reporters: “In recent weeks we’ve had to impinge on historic liberties to protect our NHS and our loved ones and yet our goal must be freedom.
“Freedom from the virus, yes, and we will not lift measures until it is safe to do so.
“But also we care about the restoration of social freedom and economic freedom too – each citizen’s right to do as they please.”
Some 18,000 contact tracers will be in place by mid-May to track those who have come into contact with an infected person, he added.
Meanwhile, the NHS has urged people to keep appointments for vaccinations such as the MMR jab.
There has been anecdotal evidence that people are staying away from hospitals and doctors due to fear of being infected with the coronavirus.
Public health minister Jo Churchill said: “If you need to visit your GP, parents should be reassured that going to a medical appointment is classed as essential travel as long as no one in the household is displaying COVID-19 symptoms.”
