The Health Secretary said he understood how frustrating it was for teachers and parents to have no firm date to work towards, but it would be wrong to speculate.
Children are not thought to be at a high risk from coronavirus, but can spread it rapidly throughout the populations, scientists think.
Year 6 primary school pupils are set to be the first ones back in the classroom, followed by year 12.
Government insiders have said they intend to start reopening these age groups in June, but no date has yet been set.
Some may not go back before the summer holidays at all, and will continue to learn at home.
Mr Hancock said: “We are considering now how we can get that restarted in a safe way.”
And he added: “It’s too soon” to set a date for sure.
“I know it’s frustrating,” he added.
His three children – 6, 12 and 13 – are being taught by his wife at home, who understands the strains it can cause.
“We know it’s imperfect, but thanks to technology it’s better than it might have been.
“I admire children who want to get back to school.”
When pressed on whether that might mean schools were shut until September, he said: “It’s just so important that we get the rate of transmission down.
“If there is something we can do before then, we will, but I can’t make any promises.”
Schools have opened in some other European countries.
And he said that the scientists don’t yet know if Brits are going to stick to lockdown measure sin the long term, which may have an influence on the schools decision.
The Health Secretary said he hoped to have more of a clue about schools and colleagues reopening in the “next couple of weeks”.
Mr Hancock said that schools “really had to” be shut back in March to stop the spread.
He said: “Although children don’t suffer from the consequences of corona anywhere near as much as adults, there have been a small number of small cases.
“By and large children are still not going down with the disease, but they still spread it.
“Lots of people from different households come and mix, that proves to be a real spreader.”
It comes after Dominic Raab said yesterday that opening all schools for all pupils at the same time would risk overwhelming the NHS with a second spike.
Nicola Sturgeon has suggested that classrooms may have to be redesigned in future, too, to keep pupils apart.
Her blueprint for schools yesterday insisted that many pupils will have to continue learning at home for months to come.
Not all pupils will be able to come in at once and still stay 2m apart.