The Reagan administration will decide soon, possibly by the end of this month, whether a renewed effort the United States is warranted to win South Africa's approval of a plan for the independence of Namibia, a senior State Department official said yesterday.

Chester A. Crocker, assistant secretary of state for African affairs, told the House subcommittee on Africa that it is too soon to tell whether such an effort would be worthwhile.

"But this administration has a very full foreign policy agenda, the implication of which is that we will not engage ourselves int he Namibia equation if we feel the prospects for success are bleak," he said. "We have been frank with allour interlocutors on these points.

"Our approach is realistic. The United States will not permit its energies, time and crdibility to be frittered away on a drawn-out and fruitless diplomatic charade in southern Africa."

The testimony was the first public statement on Namibia by the administration since Crocker and Deputy Secretary of State William P. Clark visited southern Africa last week as part of the attempt to assess the prospects for success should the United States and other Western nations mount a new Namibian independence effort.

Namibia, also known as South West Africa, is a mineral-rich former German colony between South Africa and Angola. South Africa has administered the country since World War I under a League of Nations mandate and has refused to comply with a U.N. resolution calling for it to evacuate the territory.

In January, South Africa rejected a plan for U.N.-supervised elections in Namibia on grounds that the United Nations is too sympathetic to the South West Africa People's Organization (SWAPO), a Soviet-armed movement with which it has been fighting a guerrilla war.

The administration is anxious to improve relations with the white-controlled South African government in order to counter Soviet influence in that region, but it does not want to antagonize the nations of black Africa.

It has taken a softer line toward South Africa than the Carter administration did, suggesting, for example, the possibility of incentives for South Africa in return for its cooperation in working toward an independence plan for Namibia.

This approach was criticized yesterday by Donald F. McHenry, U.S. ambassador to the United Nations in the Carter administration, who followed Crocker before the committee.

McHenry said efforts to arrange elections in Namibia have failed because South Africa is convinced that SWAPO, rather than one of the local groups the South Africans support, would win the election, and it therefore has adopted a strategy of endless delay.

As for the incentives, which reportedly include a mutual increase in defense attache personnel at the U.S. and South African embassies and permission for South Africa to open additional consulates in two American cities, McHenry said the South Africans are not likely to soften opposition to an independent Namibia just "because we throw them a carrot or a bone."

"What is likely," he added, "is that they will gulp up all of the carrots and ask for more."

In his testimony, Crocker stressed that South Africa's cooperation, however, it is obtained, is the key to gaining independence for Namibia.

"There is not going to be a Namibian settlement unless South Africa agrees to it," he said. "That is the reality."