It said ministers have written to secondary schools asking them to prepare to potentially replace isolation rules with testing.
The move comes as concerns grow about the rising number of children who have to quarantine because they are the contacts of confirmed cases
Currently children have to self-isolate for 10 days if another pupil in their bubble tests positive for coronavirus.
It has resulted in a sharp rise in pupils off school for Covid-related reasons, with the latest official figures showing 239,000 children in England missing classes - as the numbers trebled in the space of a week.
Official figures on Monday showed another rise in infections, with almost 23,000 lab-confirmed cases - the highest daily rise since January 30.
They came amid continuing concern over the spread of the Delta variant, with Portugal, Spain, Malta and Hong Kong announcing new restrictions on tourists from the UK.
Despite the increase, Health Secretary Sajid Javid said there is “no reason” why the final stage of lockdown lifting in England should not go ahead as planned on July 19.
A spokesman for the Department of Education said: “We are provisionally asking secondary schools and colleges to prepare to offer on-site testing when students return for the new academic year, so that schools are ready in case it is needed to keep as many children as possible in face-to-face education.
“We will provide further details about the approach to protective measures and test and trace in education from September in due course.”
Mr Javid said he has asked for “fresh advice” on the issue, adding that the policy is “having a huge knock-on impact” on children’s education.
“I will hopefully be able to say more on this as soon as possible,” he said.
Schools minister Nick Gibb said the Government is carrying out a review into using testing to end self-isolation for school pupils in bubbles.
Mr Gibb said: “We are conducting trials of daily contact testing as a possible alternative to self-isolation."
Mr Gibb said that a decision will be taken before July 19.
He said: “What matters also is that we keep the school safe and, if you go around our schools, you will see a raft of measures to reduce the infection rates within schools.
“There’s extra hygiene, there’s staggered breaks, we keep children in bubbles, and there’s extra ventilation in classrooms to minimise the risk of transmission.”
He said that about three per cent of students are currently self-isolating, but added that this figure is lower than it was in the autumn.
Professor Adam Finn, from the Joint Committee on Vaccination and Immunisation (JCVI), said children “don’t get ill very much when they get this infection so the harm that’s done to them by closing schools or by excluding them from schools far exceeds any harm they get from the virus itself”.
He said there needs to be a “balanced response”, adding that “anything that can be done to minimise the disruption to children’s education is a good thing as far as I’m concerned”.
It came as the new Children’s Commissioner for England said bubble arrangements and self-isolation for school pupils should end soon.
Dame Rachel de Souza said there is an urgent need for children to get back to normal as lockdown restrictions have been a “real trauma” for many young people.