President Reagan has put off a decision on whether to turn the Department of Education into a large, sub-Cabinet foundation to give his lobbyists a chance to sound out key members of Congress on the idea.

But the proposal, which the administration considers the most attractive politically, has generated little enthusiam and already has been referred to as "the worst of both worlds" because it satisfies neither the supporters of the department nor those who want it abolished.

A decision memo prepared for a White House meeting last Friday said the foundation option "is more viable in political terms" than a plan to disperse the department's programs "because the amount and intensity of opposition will be less." It also noted that those who voted in 1979 to establish the newest Cabinet department, including the key committee chairmen, Sen. William V. Roth Jr. (R-Del.) and Rep. Jack Brooks (D-Tex.), "will be in a far less difficult position if they are asked to support a foundation . . . . "

The memo, printed Monday in the trade newspaper Education Week, also said that the foundation idea would fulfill the president's promise of "abolishing" the department. But it acknowledged that conservative legislators and other critics "might claim the department has not really been eliminated, only changed in name and dropped from Cabinet status."

Anne Graham, assistant secretary of education for legislation and public affairs, said yesterday that "critics will have a problem with any alternative. If the foundation option is chosen, many would argue it's a rational approach to reducing federal regulation, while maintaining a structure to escalate the move to block grants."

The proposed foundation would keep nearly $11 billion in education programs, transfer $1.5 billion to other departments, and eliminate several small programs totalling less than $150 million.

Dismantling the department has become a symbolic test of the administration's will in some conservative circles. In a recent direct mail campaign, for instance, Sen. Roger W. Jepsen (R-Iowa) sought support for abolishing the department.

But Roth and Brooks, whose committees will have jurisdiction over any proposal to dismantle the department, have both said recently that they continue to support a Cabinet voice for education. A Roth aide said yesterday, "The senator has little enthusiasm for a drastic reorganization of the department or for dispersal."

Brooks, speaking through an aide, said he had not seen the foundation proposal but added, "I certainly wouldn't look with favor on any proposal that would return to the fragmentation and duplication of effort we tried to avert by creating the department."

In the past, Brooks has said he considers the effort to kill the department the first step in a plan for ending all federal aid to education. The decision memo notes that a foundation "would be an effective vehicle for continuing to move to a more restricted federal role," but doesn't make clear whether the reference was to restricting federal regulation or financial aid.

Sen. Robert T. Stafford, (R-Vt.) chairman of the Senate Labor and Human Resources education subcommittee, echoed Brooks' concerns in remarks yesterday to the National Education Association's legislative conference here. He also said the administration shouldn't send up any dismantling legislation until 1983, and added that his staff was on guard for any administration "end run" around the full legislative process.

Terry Herndon, executive director of NEA, which lobbied hard to create the department, said yesterday that the administration's attempt at compromise "will win the wrath of everyone."

The decision memo said the foundation would keep the biggest chunks of the department's programs, including college grants and loans, Title I aid for low-income children, current and proposed block grants, and the office of civil rights. Rehabilitation services for the handicappped, impact aid and Indian education programs would be transferred to other departments.