The Carter administration will try to head off congressional pressure for a college tuition tax credit by expanding federal aid for students to include more middle-income families.

Although details have not been worked out yet, White House officials have earmarked between $500 million and $700 million in contingency funds in the fiscal 1979 budget for enlarging current student grant programs.

Officials of the Treasury and Health, Education and Welfare departments are scheduled to argue for the grants-first strategy Thursday at a hearing of the Senate Finance subcommittee on taxation and debt management.

Administration planners are expected to iron out details of their proposals sometime next week. Officials said the final price tag would be "competitive with" the most popular tax credit plans.

The purpose is to sidetrack the tuition tax credit proposal, which administration planners consider too costly and inefficient. Tax experts say many of the benefits of a credit would go to upper-income persons.

The battle over whether to enact a tuition credit held up passage of the Social Security bill last month after Sen. William V. Roth Jr. (R-Del.), the measure's major sponsor, insisted on the rider in conference committee.

Roth ultimately agreed to drop the issue temporarily to permit enactment of the Social Security measure, but vowed to bring it up again this session. A spokesman for Roth said yesterday the senator still would press for the credit.

The Roth proposal would cost the Treasury $1.3 billion a year in lost revenues. The provision would allow parents to reduce their federal income taxes by up to $250 for each child in college, depending on tuition and costs.

A more generous tuition-credit proposal sponsored jointly by Sens. Daniel P. Moynihan (D-N.Y.) and Bob Packwood (R-Ore.) would cost as much as $4.5 billion. It would allow a tax reduction of $500 a student.

The proposals the administration is considering first would liberalize the existing "basic educational opportunity grants" for the needy to include more middle-income families, and strengthen federal loan guarantee plans.

Officials said they also may try to boost spending for three other student grant programs that already serve some middle-income students - the work-study program, state scholarship program and "supplemental" grants program.

A new report by the Congressional Budget Office shows that liberalizing grant programs would be more "efficient" than a tax credit in reaching middle-income families because it would not aid upper-income youngsters as well.

Roth and other proponents of the tax credit have sought to portray the proposal as a form of tax relief for the middle class. However, tax experts say the provision would benefit many upper-income families.