The idea was attacked by left- wing Labour MPs as threatening to break up the national welfare system. But Mr Field, who was promoted from the back benches to "think the unthinkable" about welfare reform by Tony Blair, that warned Labour could not fulfil its pledges without radical action.
Mr Field said during a tour of social security offices in Exeter, Devon, that there could be savings of pounds 15m on the local social security budget of pounds 170m if it was managed locally.
Under the present system, there was no way he could say to the local office, "Is it feasible if you managed it in your own way rather than us telling you how to manage it that you could take pounds 15m out of the budget within the life of a Parliament?".
That money "could go, for example, into schools in Exeter or further education - whatever was thought to be the right way of moving from welfare dependency to creating opportunities", Mr Field added on BBC radio.
Asked if he wanted to see local areas given autonomy over their budgets, he warned: "If it doesn't happen, I don't see how we are going to be able to deliver the sorts of reforms that we want to deliver. So it's clearly got to be on the agenda. Quite how we do is the next stage."
Jeremy Corbyn, a left-wing Labour MP, said the idea that social security offices should get involved in education was "bizarre".
He warned that it would worsen the existing system which was already a lottery, where benefits were available in some areas but not in others.
"What Frank should be looking at is the housing shortage, the poverty trap and the vast expenditure on housing benefit on landlords and bed and breakfast accommodation. Those are the areas where we could save money.
"The idea of devolving budgets to regions seems to be breaking up the idea of a mandatory award system in social security," Mr Corbyn said on BBC radio.
The Liberal Democrat social security spokesman, Steven Webb, welcomed Mr Field's "innovative approach to welfare reform". Mr Webb, the MP for Northavon, added: "We always welcome new thinking, especially where it involves devolving power to local people."
But he warned too that the locally administered Social Fund, which provides loans and grants to people on benefits, was "well-known for being a lottery".
Mr Webb added: "We cannot risk a situation in which benefits in different parts of the country may run out before the end of the year."
Paul Connery, of the Unemployment Unit, warning of "potential pitfalls", said: "The social security budget is very inflexible. They are spending about pounds 93bn right now of which only pounds 3bn is running costs and administration.
"So they have to bite into the benefit bill itself. And the difficulty is that much of these benefits are mandatory entitle- ments.
"People get them because they are unemployed, they are on low earnings, they are single parents or they are retired people who don't have sufficient income. That is going to be very difficult to dig into."
Jim Hanson, national officer of the Civil and Public Service Union, whose members would have to implement the idea, said many staff were already subjected to abuse and violence from claimants.
"At the moment at least we can say that these levels are not determined by the staff, they are determined by Parliament. But if they are determined by the staff in the offices, then we are going to find people wanting to take it out on them if they're not satisfied," he warned.Reuse content