It is hoped the vaccination programme could begin in September
Children in five English cities could become the first to receive vaccines for swine flu.
Bristol, Exeter, Oxford, Southampton and part of London are proposed sites for a trial for children aged between six months and 12 years old.
A proposal for funding has gone to the NHS National Institute for Health Research for approval.
If successful, the voluntary trials would begin in September on 800 to 900 children.
Participation in the scheme would be voluntary and consenting parents would be briefed on the possible risks before signing a release form.
A UK adult vaccine trial began in Leicester last week.
Bristol University professor of paediatrics Adam Finn and colleagues have put together the funding proposal for Bristol and Exeter.
Prof Finn said the two vaccines being trialled were "unlikely to produce any serious side effects in children".
He said the trial would help the Department of Health make decisions on vaccination programmes, as there is currently no information on how effective the vaccines would be in children.
He told BBC News Online: "We will be able to provide information on how well the vaccines work.
"If you look at the cases of people who are sick enough to be in hospital or die, the proportion of those cases who were younger is higher than we would normally see in seasonal flu.
"That gives us a reason for doing this study."
The cost to the NHS would be "several hundred" pounds per person.
"The advantage is that it's quite likely that people are going to have to make decisions about using these vaccines.
"It will be of great help to have some effective evidence to help get those decisions made."
The first swine flu vaccines are expected to be licensed for use in the general population in September.
Ministers have repeatedly said they expect to have enough doses for half the UK population by the end of the year but advisers are still finalising plans on who would be first to get the injection.
Department of Health spokesperson said: "The National Institute for Health Research is making a decision and applicants will be notified in writing shortly."