Former Massachusetts Governor Michael S. Dukakis may accept a teaching and administrative post at Harvard, a source close to Dukakis said last night. The source did not, however, confirm reports that Dukakis has definitely decided on Harvard, saying he is considering various offers from area universities.

WNAC-TV reported late last night that a source close to Dukakis said the former governor had accepted an offer from the Kennedy School of Government, but Jonathan Moore, director of the Institute of Politics, refused to confirm or deny the report late last night.

Other Kennedy School officials yesterday refused to say whether Dukakis had accepted a position at the University. Graham T. Allison, dean of the Kennedy School, could not be reached for comment last night.

Richard Giesser, former campaign manager for Dukakis, and Peter Lynch, former assistant campaign manager, last night refused to confirm or deny the report.

If Dukakis comes to Harvard he would follow in the steps of his predecessor, former governor Francis W. Sargent. Sargent taught a seminar at the Institute of Politics following his defeat by Dukakis in the 1974 general election.

Officials at the Institute of Politics, however, have said that Dukakis will not serve as a Fellow of the Institute, leaving open the possibility that he might accept a post at the Kennedy School.

Dukakis was defeated in last September's Democratic primary by Edward J. King, who went on to become governor. King defeated the one-term Dukakis in a closely contested race that centered on the issues of taxation and crime.

One-term Governor

Dukakis, who gained prominence as moderator of the WGBH-TV award-winning "Advocates" series, assumed the governorship in January 1975, after defeating Sargent.

Dukakis inherited a large budget deficit from Sargent. He alienated much of his support among Massachusetts liberals by cutting social welfare programs in efforts to deal with the state's money problems.