The Department for Education and Skills (DfES) confirmed that it was considering a ban after local authority education directors raised the issue. A spokesman said the new School Food Trust would address the issue.
Over the last few weeks, DfES officials have held a series of high-level meetings with local education directors to discuss a possible ban.
Chris Waterman, the executive director of the Confederation of Education and Children's Services Managers, was present at the meetings.
He told Children Now: "If children can walk across the playground and buy chips and burgers from a van instead of using the school meal service then that undermines that service. What we want to see is exclusion zones set up around schools to prevent these chip vans from effectively asset stripping school meal services."
Waterman also called for action to stop local fast food shops from offering cheap lunchtime deals to pupils. He said: "We're asking for some sort of voluntary code so these shops don't compete for pupils' dinner money."
The charity 4Children supported a ban on fast food vans. Chief executive Anne Longfield said: "Chip vans should not be outside schools. While food like that is readily available and targeted at children, then it's going to be much more difficult for those parents and teachers who are trying get children to eat healthily.
"It also makes it more difficult for children themselves. A lot of children want to eat healthily but find that when they are faced with a half-hour queue for lunch or a chip van outside, and all their friends are going to the van, then it's very difficult to say 'no I'm going to wait in this half-hour queue'."
It is understood that the DfES is keen to clamp down on chip vans and could use the new Education and Skills Bill, expected to be announced in Queen's Speech yesterday (17 May), to introduce a ban.
The department refused to comment on the Queen's Speech and emphasised the role of the School Food Trust instead. A spokesman said: "This is an interesting point and something that the new School Food Trust will no doubt want to consider alongside the range of issues that it will be looking at."
