The White House is considering removal of Martha A. McSteen as acting head of the Social Security Administration and nomination of Dorcas R. Hardy, now an assistant secretary of Health and Human Services, to head the agency, government sources said yesterday.

McSteen, 60, who has been with the agency since 1947, was its southwest regional commissioner when HHS Secretary Margaret M. Heckler promoted her to acting commissioner 16 months ago.

Heckler had asked the White House to nominate McSteen to fill the job on a permanent basis, but the White House never sent McSteen's name to Capitol Hill, despite judgments by many in the HHS and on Capitol Hill that she has performed the job well.

Sources said the White House viewed the post as a major policy appointment that should be filled by President Reagan's choice rather than a career employe like McSteen. They said the White House wanted to make a new start at the agency with its own nominee.

Hardy, 38, was assistant secretary of the California health department when Reagan was governor of California. In 1981, he nominated her as assistant secretary of HHS for human development services. She is considered to be a good administrator, a conservative and in tune with the president's views on the need to cut outlays for some social programs.

In 1983, for example, she proposed cuts in federal support for foster children and cuts in grants for sheltered workshops, group homes and early screening of disabled children.

In 1983, Hardy was the focus of a controversy over three grants totaling $493,000 that her office awarded to the Center for Health Sciences Research at the University of Southern California Medical School, where Hardy had worked before joining the HHS.

In a Sept. 27, 1984, report, the General Accounting Office said Hardy had created "the appearance of a lack of impartiality" by participating in the decisions to award the grants to USC. In two of the three cases, the USC grant applications were given preference over applications that had received higher rankings from experts in the field. But the report concluded that her involvement was not "improper."

White House sources said last week that its personnel office has been trying to find someone to fill the Social Security job for some time.

"We have ended a long search for a nominee," one source said, adding that Hardy's nomination is all but locked up. Other sources said Heckler wants McSteen in the job, however, and it is conceivable that she may thwart a change.

HHS press spokesman Claire del Real said only that Hardy "is under consideration," but another source said "you can bet it's going to be Hardy."

Although Hardy is an assistant secretary, her current domain is tiny compared with the Social Security Administration. The Office of Human Development Services, which has a budget of about $6 billion, handles programs for children such as Head Start, as well as programs for the aged and Indians.

Social Security, which administers the Social Security, Aid to Families with Dependent Children and Supplemental Security Income programs, among others, has more than 79,000 full-time employes and disburses more than $200 billion a year to more than 50 million people.