The Government expects reception, year one and year six children in England to be able to return to the classroom on June 1 at the earliest.
But it has emerged that a number of schools in the county have reservations about the plan.
At a meeting last week those concerns were aired and Shropshire Council has agreed that there may need to be a "phased" approach to meeting the government's plan.
Telford & Wrekin Council is yet to make its position public, with talks ongoing.
But Government ministers have admitted there is unlikely to be a “uniform approach”, opening up the possibility of each school being judged on its own merits.
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At Shropshire Council, Karen Bradshaw, executive director of children’s services and acting interim chief executive, said that some schools need time to come up with a different approach due to staff absences, small classrooms, and difficulties with school layout.
She said that it was agreed that any decisions taken by schools should be driven by their own risk assessments.
One letter from a school to parents said the council had agreed to back decisions by headteachers and governing bodies from some schools who are not happy with the government proposals as they stand.
It is understood the schools affected are drawing up their own plans for re-integrating pupils.
Mrs Bradshaw said: "A meeting took place between school representatives and Shropshire Council officers last Thursday to confirm the agreed approach across Shropshire.
"The meeting and subsequent communication with schools stated that school decisions should be driven by risk assessment at school levels.
"We agreed that schools should pay attention to government guidance and the prioritisation of different groups but there may need to be a phased re-integration that works towards the government’s ambitions.
"Factors which may lead to a localised approach may include staff absence, smaller than average classrooms, school layout and so on.”
Telford & Wrekin Council leader Shaun Davies said: “We are working really closely with our schools, our headteachers, our governors, and the unions, to make sure that those schools that do reopen are as safe as can be. We will have further things to say on this in coming days.”
Meanwhile there is still no update on if and when students can return to the classroom in Wales. Welsh Education Minister Kirsty Williams said that when they are planning to reopen, she will be the first to make an announcement. But, at the moment, there is still more work needed on managing the safety of the situation before schools will reopen.
She said any decision would have health and wellbeing of staff and children at the forefront. She said it will be impossible to give 100 per cent guarantees but it was incumbent that they manage risks as much as possible.
The developments come amid an ongoing row between unions and the government over its plans to reopen schools.
Shropshire Star readers have also voiced concerns with nearly 60 per cent of more than 5,000 respondents to a survey saying they feel it is unsafe for children to return to school during the coronavirus lockdown.
Paul Whiteman, general secretary of school leaders' union NAHT, said primary school staff wanted more clarification on whether schools would have high transmission of the illness.
He said: "Specifically around the transmission from children to adults, we've been told over the weekend – it's been asserted by the Government publicly over the weekend – that there isn't the level of risk that we fear.
"However, we haven't yet seen the scientific underpin of that."
We are ready to welcome children back into class
“Trust the headteachers and communicate with your school”. That was the message from Sarah Godden, headteacher at Oldbury Wells School, who was helping to measure up at St Leonard’s Primary School, both in Bridgnorth, as part of her role as CEO of the TrustED Schools’ Partnership.
The group includes six primary and secondary schools, which are all currently in “limbo”.
Ms Godden said primary schools in Shropshire are “largely ready” for a phased reopening and teachers have been working “intensely” to implement new ways of learning. But she said the safety of teachers, students and their families must remain a priority.
“Primary colleagues are working very hard to be ready to open, if that’s what is asked of them,” Mrs Godden said. “They’ve been very careful and thorough with the plans they’ve put in place.
“They’re all looking at staggered starts so not all children will arrive at the same time.
“It’s also very important to realise a lot of schools have remained open for children of key workers and the vulnerable through lockdown, so they’re already in the habit of working with new systems in place and social distancing.”
Mrs Godden said she had “mixed feelings” as she was desperate to get children back but was also mindful that it should be done “exceptionally carefully”.