Archbishop Vincent Nichols made the comments during a breakfast with more than 80 school children from St Mary's and St Michael's school in Tower Hamlets, London last week.
"I would love to see every school without a hungry child in sight," he told The Times. "If that's what it takes, then yes, let's do that."
The breakfast was provided by the charity Magic Breakfast and the Catholic social action agency, Caritas Westminster, as part of a collaborative initiative to provide free, healthy breakfasts to primary school children.
Five Catholic schools in Westminster Diocese, including St Mary's and St Michael's, are taking part in the scheme.
Free school meals are currently provided to children whose parents receive benefits or earn less than £16,190 per year, but last week the Deputy Prime Minister and Liberal Democrat leader Nick Clegg announced a £600 million plan to expand this to all children in their first three years at school.