James Schlesinger, who has served in the Cabinet under three presidents, is among nearly a dozen people rumored to be in contention for the post of energy secretary in the Bush administration.

Schlesinger would fit the president-elect's desire for someone with a nuclear background to tackle the department's massive cleanup and modernization at its 17 weapons plants in 12 states.At least 10 other names still were circulating around Washington's rumor mills.

Schlesinger's was a new name as a possible selection. Two other candidates, Lee M. Thomas, administrator of the Environmental Protection Agency, and former Louisana Rep. Henson Moore, also remained in contention.

Now a consultant and staff member of the Center for Strategic and International Studies, Schlesinger served as defense secretary under President Nixon and was dismissed from that job President Ford in 1975. His resignation was one of a handful President Carter accepted in 1979 after demanding resignations from the entire Cabinet and top echelons of his administration.

Schlesinger had the misfortune to be energy secretary when the Iranian revolution triggered gasoline lines in much of the United States - lines many analysts, including the current secretary, John Herrington, believe were the result of price and allocation controls in effect then and no longer on the books.

Other names mentioned are:

-Democrats JOHN DEUTCH, provost of Massachusetts Institute of Technology, and JOHN AHEARNE, former chairman of the Nuclear Regulatory Commission and chairman.

-MARTHA HESSE, deregulation-oriented chairman of the Federal Energy Regulatory Commission, and former assistant energy secretary for administration.

-PETER JOHNSON, former head of the Bonneville Power Administration and the candidate backed by Sen. James McClure of Idaho, senior Republican on the Energy Committee.

-Retiring Sen. DAN EVANS of Washington, who has been opposed by McClure, and former Gov. LAMAR ALEXANDER of Tennessee.

-Air Force Lt. Gen. JAMES A. ABRAHAMSON, retiring head of the Pentagon's space-defense program and former head of the F-16 fighter and the space shuttle programs.

-Former Rep. JAMES BROYHILL of North Carolina, senior Republican on the House Energy and Commerce Committee before losing a Senate race in 1986.