Health service officials are compiling planning documents which include a measure to offer a single dose of the Pfizer jab to children aged 12 and older when the new school year starts, according to The Sunday Times.
Pfizer has said trials of its vaccine in children aged 12 to 15 showed 100% efficacy and a strong immune response.
The plans, which the Times said it had confirmed with government and NHS sources, are contingent on advice from the Joint Committee on Vaccination and Immunisation (JCVI) due this summer.
Committee member Professor Adam Finn, from the University of Bristol, told the Times: "We need to be in a position to immunise children, particularly teenagers, promptly and efficiently if we need to.
"It is extremely important that education in the next academic year is not disrupted in any way," the paediatrician said.
But he added: "We should only be doing vaccine programmes when we need to do them."
Prof Finn told Times Radio on Sunday it was "very much an open question" whether secondary school pupils will need to be vaccinated from September.
While children are unlikely to fall ill with Covid-19, they do play a role in transmitting the virus.
Prof Finn said on April 24 that children had been frustratingly "left behind" in the Covid-19 vaccine programme, adding he wanted to "get on" and conduct the necessary trials in children.
A spokeswoman for the Department of Health and Social Care (DHSC) said: "No decisions have been made on whether children should be offered vaccinations and we will be guided by the experts once clinical trials have concluded.
"As we’ve already said, we are preparing for a booster programme to take place from the autumn and we continue to plan for all scenarios.
"We have hit our target of offering vaccines to everyone in phase one of the programme and we are on track to offer a jab to all adults by the end of July."
People over the age of 40 were invited to book their first appointment for a Covid-19 vaccine on Friday April 30, after it was revealed that more than 88,003 people had been given their first dose of a Covid-19 vaccine across Peterborough.
Over 34,000 have also been given their second dose and so are considered fully vaccinated.