If Daniel Patrick Moynihan remains at Harvard next year, he will be allowed to offer courses in the Government Department. The Government faculty extended the urbanologist an invitation to teach in the department at a meeting on Thursday,

Moynihan was interviewed for a teaching position at Cornell on April 15, and sources on the Cornell faculty reported last week that he had been offered the John L. Senior Professor ship of American Institutions. Cornell's most prestigious-and highly paid-faculty position.

Moynihan was unavailable for comment on the offer last week, and yesterday his office told reporters that he was sick at home and unable to speak to them.

Washington Man

Moynihan, who is a professor of Education and Urban Studies at the Ed School. returned to Harvard last February after two years as President Nixon's urban affairs counselor. While still in Washington, he had told interviewers that he expected to be offered a post in the Government Department upon his return to Cambridge, but he received no such invitation. He has discussed the Cornell offer with several friends in the Government faculty.

A spokesman for Cornell yesterday denied that Moynihan has been offered the post, stating that "the faculty committee reviewing the Senior Professor ship has not yet sent its report to the President." The approval of the Cornell President and Board of Trustees, however, is usually viewed as a formality in faculty appointments, and the actual decision on the offer would be made by the faculty committee before it consults the President.

Samuel P. Huntington, Thompson Professor of Government and Chairman of the Government Department, explained yesterday that the new invitation will not affect Moynihan's status as a professor of Education. "We've invited him, if he's at Harvard and he feels inclined, to offer a course or courses in the Department. This has nothing to do with his title."

Denies Attempt

According to Huntington, the issue of allowing Moynihan to give Government courses has only come up within the past month, but he denied that the offer was an attempt to keep Moynihan from going to Cornell.

"Moynihan has a degree in political science, so I don't consider this unusual," Huntington said. "The question hadn't been raised curlier, although it could have been," Moynihan received a Ph.D. from the Fletcher School of Law and Diplomacy at Tufts in 1961.

Before leaving Harvard to join the Nixon administration in 1969, Moynihan was director of the Harvard-M.I.T. Joint Center for Urban Studies. He did not resume that position when he returned to Cambridge three months ago. He has published widely in the field of urban affairs, and was co-author with Nathan Glazer. professor of Education and Social Structure. of Boyond the Mclting Pot, a highly publicized work on the assimilation of ethnic minorities.

Criticized

Some of Moynihan's other writings have been less well received. He was severely criticized last year after the publication of a memorandum to President, Nixon urging "benign neglect" of blacks, and his theory of matriarchal domination in black families has also me; with controversy.