Some school pupils may be stuck at home until at least February, with the Government under growing pressure to abandon plans to re-open next month.
Teaching unions are among those urging ministers to reconsider amid concerns students will catch the new Covid variant and cause cases to spike.
Members of the Government's Scientific Advisory Group for Emergencies (Sage) have also reportedly told ministers schools reopening could cause infections to spiral - even if another national lockdown was introduced, according to the Telegraph.
Earlier this month, the Government said exam-year students would go back to school as normal after the Christmas holidays, but the majority of secondary school pupils would start the term online to allow headteachers to roll out mass testing of children and staff.
A meeting was held between ministers, Downing Street officials and the Department for Education on Monday to discuss the plan further, but the DfE would not comment on its outcome.
The Times reported Health Secretary Matt Hancock and Cabinet Office minister Michael Gove were among those who suggested that a delayed reopening would be necessary, while Education Secretary Gavin Williamson wanted to "push ahead" with the current plan which involves mass testing of students.
The Telegraph also reported that Sage advisers have suggested that keeping the majority of schools closed in January may keep the R number, the rate of infections, below one.
Last week scientists warned PM Boris Johnson he should keep secondary schools closed throughout January, with the possibility of a national lockdown, Politico reports.
It comes as the Ministry of Defence (MoD) announced that 1,500 military personnel would be deployed to support the implementation of the testing systems to allow pupils to return.
Dr Patrick Roach, general secretary of the NASUWT, wrote to the Education Secretary on Monday demanding further action on school safety.
The letter urged Mr Williamson to allow schools to move to remote learning for all pupils, except those deemed to be vulnerable or the children of key workers, in the highest tier areas.
The union is also asking the Government to publish new safety guidance in light of the new Covid-19 variant, introduce mandatory face coverings within schools and give staff priority access to the vaccine.
Mary Bousted and Kevin Courtney, the joint general secretaries of the National Education Union (NEU), have also written to Mr Williamson, along with Mr Johnson, reiterating calls for schools and colleges to remain closed for at least the first two weeks of January, except for vulnerable children and the children of key workers.
The letter asks the Government to share the evidence and advice received from experts about schools reopening from the chief medical officer.
"You certainly cannot expect education staff to show good will towards your plans for education if you do not at least share all the information you have about this dreadful disease with them," it states.
Mr Gove said he was confident schools could reopen in the new year with a staggered approach, with primary school pupils and Year 11 and Year 13 pupils returning in the first week of January, and other students going back later in the month.
Defence Secretary Ben Wallace said that the armed forces had been put on standby to help put the testing systems in place.
The majority of the personnel will form local response teams, providing support and phone advice to institutions needing guidance on the testing process and set-up of the testing facilities.
