Secretary of Education Terrel H. Bell has recommended that President Reagan abolish the Department of Education and turn over its functions to a new federal foundation of less than Cabinet rank government sources said yesterday.

No programs would be immediately affected, but a transformation of this kind would nevertheless be in line with the president's campaign promise to dismantle the department created by President Carter and diminish the federal role in education.

Bell's recommendation was contained in an option paper sent to the White House Tuesday. The paper reportedly listed at least four major ways of abolishing the department, with Bell indicating the one he more radical. The administration hopes to make its decision and send a reorganization proposal to Congress late this year.

One option, which Bell indicated he did not favor, was to merge the Department of Education into another Cabinet department such as Health and Human Services, Labor or Commerce. Bell has long opposed this idea and is known to have felt deeply frustrated where he was commissioner of education in the old Department of Health, Education and Welfare, at a time when many education progrmas were in that department but the commissioner was in a subordinate role.

Another option, which Bell reportedly also did not endorse, was to kill the education unit entirely and disperse its functions among other agencies, such as student loans to Treasury, vocational rehabilitation to HHS, vocational education to Labor and possibly civil rights enforcement to the Justice Department. A presidential adviser on education would then be placed on the White House staff to coordinate and advise the president on policy matters.

A chief option was to convert the existing department into an independent agency without Cabinet tank; this would be similar to the foundation idea Bell came out for. But designating the new unit an independent agency, it was felt, implied it would permanently retain all its functions.

The fourth and favored option was to convert the existing department into a foundation. Most functions would be retained for now, though the option paper raised the possibility of sending the guaranteed student loan program to Treasury. Later, under this alternative, most of the main federal education programs could be spun off to the states through block grants or to other federal departments. This would leave the National Education Foundation, like the National Science Foundation, an agency devoted largely to research and the gathering of statistics.

Bell was in Denver for his son's wedding and could not be reached for comment, and Gary Jone, the deputy undersecretary in charge of developing the option plan, declined to comment.

But another knowledgeable administration source said that all the options assume that at some time in the future, some of the larger programs now administered by the department, such as the $1 billion education-for-the-handicapped program, would be handed over to the states, an administration proposal which Congress rejected two weeks ago but which is expected to be renewed next year.