Schools in England will aim to start to reopen at the beginning of June as part of Boris Johnson's draft plan to lift the lockdown.
The Prime Minister is understood to have drafted a 50-page plan to get the UK back to normal over the next six months.
One step of the five-stage plan would see a phased return of primary schools, starting with Year 6, at the end of May or beginning of June.
This would be followed by a phased return of secondary schools at the end of June, before the summer holidays.
Mr Johnson will set out his “roadmap” on Sunday.
He said the first steps will happen the next day “if we possibly can”.
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The Government's blueprint aims to to relax the lockdown in staggered steps between now and October.
However, officials fear a second wave of coronavirus or a seasonal flu outbreak this autumn could blow their plans off course.
A Government source told the Mirror: “It’s a bit of a shambles.
“Nobody can quite agree what to do and when to do it. Somebody comes up with a bright idea, but the practicalities get in the way.
"We’re not South Korea.”
The plans come as the UK became the first country in Europe to officially report more than 30,000 deaths.
A further 649 people have died, taking the total death toll to 30,076.
Schools in other countries have started to reopen, including the Chinese city of Wuhan, where the coronavirus outbreak started.
Many of the schools that are now open in the area have restricted the number of pupils allowed into class rooms to practise social distancing.
Students and staff approaching will be tested at school gates and thermal scanners will also be present.
Pictures from Wuhan show students wearing face masks and desks kept a safe distance apart from each other.
One student who returned to school in Wuhan posted on social media platform Weibo: "School is finally reopening.
“This is the first time that I’m so happy to go back to school, although I have to sit a monthly examination on the 8th.”
The measures could be a sign of things to come when Britain's schools reopen.
Other countries such as Germany and Denmark have also began to allow pupils to return to school, although Britain's Foreign Secretary Dominic Raab said on Tuesday that it is still to early to consider reopening schools.
Unions have warned teachers of Section 44 of the Employment Rights Act 1996, which protects an employee’s right to withdraw from a workplace if they believe it is unsafe.
Geoff Barton, the general secretary of the Association of School and College Leaders, said: "The overriding concern is that any decision is underpinned by public health and scientific advice that the timing is right, and that there is clear guidance to schools and colleges on the measures which will need to be put in place to protect staff and pupils from the risk of infection.
"It will be necessary to build confidence that it is safe to return to schools, because otherwise parents will vote with their feet, and they will not send their children to school.
"For all these reasons, we would urge that any date is kept under review, and that if more time is needed then the date is changed accordingly."
