It would be "extremely reckless" to reopen schools without including leaders in the planning stages or sharing proper safety arrangements, heads have said.
It was reported this morning that schools could reopen as early as 11 May, as part of a three-phase plan to lift lockdown measures in the UK.
But school leaders' union NAHT has said private briefings about senior ministers’ responses to the crisis "must stop", as they are "causing confusion and fear".
Coronavirus: 'Stop speculation about schools reopening'
Covid-19 response: How do we reopen schools safely?
"A return to school is not a matter for debate it is a question for science," NAHT general secretary Paul Whiteman said.
The "traffic light" proposals, which are reported to have been prepared for Boris Johnson when he returns to work, suggest that primary pupils and those in Year 10 and 12 should return to school first.
Separate age groups could then be taught on different days, or every other week, to make social distancing easier to enforce.
The Sunday Times reports that ministers will suggest schools could reopen on 11 May, 1 June, or at the start of September.
It adds that, if reopening is delayed, those set to take GCSE and A levels next year may be required to attend school during the summer holidays, while their exams could also be pushed back by two months, to July 2021.
But Michael Gove this morning denied suggestions the government had drawn up plans for a three-tiered relaxation of lockdown measures.
The Chancellor of the Duchy of Lancaster poured cold water on suggestions a "traffic light" strategy is about to be brought in which would see some schools and businesses allowed to reopen in mid-May.
Mr Gove told BBC One's The Andrew Marr Show: "We have stressed that the reporting in today's newspapers that schools will reopen on May 11, that is not true, we have not made that decision."
NAHT general secretary Paul Whiteman said it would be wrong to send pupils back to school without first sharing plans and safety arrangements with leaders.
"Any return to school must be led by the best scientific and medical advice available," he said.
"But any return to school must be planned in dialogue with the profession and be accompanied by robust safety measures for pupils, parents, school staff and the wider community.
"The current frenzy of speculation about schools clearly comes from people outside the education arena demonstrating a profound misunderstanding of schools and the education context."
Education secretary Gavin Williamson said today in a tweet that "no decision has been made" on when schools will reopen.
No decision has been made on when we will reopen schools.— Gavin Williamson (@GavinWilliamson) April 19, 2020
I can reassure schools and parents that they will only reopen when the scientific advice indicates it is the right time to do so.
Mr Whiteman said he was pleased the secretary of state had "moved to set the record straight immediately".
But he warned: “Private briefings about senior ministers’ responses to Coronavirus simply must stop. It is irresponsible and is causing confusion and fear."
Mr Whiteman added: “Schools stepped up immediately alongside other public services in response to this crisis. Not through compulsion but through a determination to play their part.
“Instructing school leaders and their teams to return without including them in the planning stages or sharing proper safety arrangements would be extremely reckless.”