President Reagan may again seek to abolish the Department of Education, a senior White House official said today.

Reagan may also attempt to renew his "New Federalism" initiative to shift federal programs "and the money to pay for them" back to the states and localities, said the official, who spoke on condition that he not be identified.

Those are two options in a broad array of second-term agenda items -- beyond the immediate business of reducing the deficit -- that are being studied at the White House.

According to the official, earlier this year Reagan asked White House counselor Edwin Meese III to develop a possible agenda for "an overall policy plan" for the president's second term. The purpose was to identify larger goals so that Reagan's policies would not be driven exclusively by the need to reduce the deficit, the official said.

The official added that one goal was to use the second term to implement, and make more permanent, many of the conservative approaches that Reagan brought to his first term.

Meese presented a series of agenda items at a Cabinet meeting last week and Reagan gave him approval to develop them further. The items, some of which may be laid out in Reagan's State of the Union and Inaugural addresses, include federalism, renewed focus on world hunger, closer cooperation in space between the government and private industry, and improved governmental efficiency, the official said. He noted that some but not all of them, such as the world hunger idea, could be identified as conservative goals.

However, all of these agenda items will probably take a back seat, at least temporarily, to the deficit-reduction and tax-simplification proposals Reagan intends to make in January, the official said.

The president vowed in his 1980 campaign to abolish the Education and Energy departments, but never succeeded, and Congess recently has been beefing up education spending. The official said Reagan believes there is a federal role in education, but no need for a Cabinet-level department.

"I don't think there's any more need for the Department of Education today than there was in 1980," the official said. Having a separate department for education programs "serves no useful purpose," he said.

"There is a federal role" in education, the official said, describing it as "providing leadership," such as that of the National Commission on Excellence in Education, which framed a national debate on improving education by issuing a highly critical report last year. The commission's widely acclaimed success has demonstrated that education can be improved without expanding the bureaucracy, the official said.

In the past, discussion of abolishing the Education Department has focused on transferring its programs elsewhere, not eliminating all of them at once. Congress, however, has stiffly resisted any such plans.

The official said Reagan had made no decision about abolishing the department, nor had abolishing it been presented to him as an option.

His comments came at a time when the administration is searching for a replacement for Education Secretary T.H. Bell, who resigned after the election. Two leading candidates were recently interviewed by a group of conservative activists.

White House officials have said Reagan intends to wait a while before making a final choice on Bell's replacement.

On federalism, the official indicated that Reagan is interested in once again trying to shift federal responsibilities back to state and local government. He said this could be done gradually, in part through the use of more block grants, which would give states more leeway to decide how to use federal funds.

The official said he thought it was unfortunate that Reagan's 1982 New Federalism proposal was "misconstrued" as simply a budgetary device. This time, he said, attempts would be made to divorce it from budget-cutting.