Former Ohio Gov. John J. Gilligan has been asked to head the Agency for International Development, Carter administration officials said yesterday.

Gilligan, 58, said in a telephone interview from his home in Cincinnati that he had discussed the post with Secretary of State Cyrus R. Vance on Wednesday and had Promised to give his answer next week. He indicated it would be yes.

The prospective appointment came as something of a surprise. Speculation about the job had mentioned the Rev. Theodore Hesburgh, president of Notre Dame University, 1972 Democratic vice presidential nominee Sargent Shriver and Henry Owen of the Brookings Institution.

Gilligan said Vance had told him his background as a governor and as a member of Congress outweighted his lack of experience overseas.

Gilligan, a graduate of Notre Dame, was elected to the House in 1964 and was defeated in 1966. In 1968. he won the Democratic senatorial nomination from incumbent Sen. Frank J. Lausche but lost in the general election to Republican William B. Saxbe, later Attorney General and ambassador to India.

Gilligan was elected governor in 1970 but lost a re-election bid in a close race with former Gov. James A. Rhodes (R) in 1974.

He spent last year in Washington as a fellow of the Woodrow Wilson International Center for Scholars.

It was also learned that Douglas J. Bennet Jr., staff director of the Senate Budget Committee, will be nominated to be assistant secretary of state for congressional relations.

Jerrold L. Schecter, chief diplomatic correspondent of Time magazine, has been appointed to handle press, congressional and public liaison for the National Security Council staff headed by Zbigniew Brzezinski.