A prime topic in the hallways of the Energy Department these days is who will replace Secretary James B. Edwards when the South Carolinian returns home to take an academic post.

Among the current favorites under consideration at the White House are Donald P. Hodel, undersecretary of the interior, and Rep. James T. Broyhill (R-N.C.). A couple of weeks ago, energy trade publications were touting Robert A. G. Monks, a director of the Synthetic Fuels Corp., and Edwards is said to favor his own deputy, W. Kenneth Davis.

Edwards reportedly asked the White House to consider Davis, even though he knew the chances of getting the Senate to confirm a third former Bechtel Group executive to a Cabinet position were slim to nil.

Hodel, too, could run into some confirmation problems, partly because of his close association with Interior Secretary James G. Watt, whose policies have raised hackles on both sides of the aisle. Hodel, former administrator of the Bonneville Power Administration, has solid political credentials (he was Reagan's 1968 presidential campaign manager in Oregon), but he is simpatico with the philosophies of his current boss and longtime friend. He has warned against "environmental extremists" and the "anti-producers, the anti-achievers."

Some environmental groups expect Hodel to stay at Interior and replace Watt if, as they speculate, the White House dumps its most controversial Cabinet member after the fall elections.

An aide to Broyhill said Edwards asked permission to put the congressman's name in the running, and Broyhill agreed. But the aide, Phil Kirk, said Broyhill doesn't expect to be named, partly because he's not lobbying for the job. "He has said it would be very difficult to turn down if he were asked by the president to accept it," Kirk said. "But he doesn't want it badly or he'd be trying to get it."

Monks is a former energy commissioner in Maine and was an executive of a bank investment management company when he was named to the Synfuels board by Reagan in May, 1981. His name made the early rounds for energy secretary before Edwards was selected.

Also apparently in the running are O. Pendleton Thomas, a former president of B.F. Goodrich Co., and Norman (Ike) Livermore, who ran the transition team at the Environmental Protection Agency. Rep. Edward J. Derwinski (R-Ill.) told the Chicago Sun-Times that the administration had mentioned the DOE job to him, too, although he characterized the discussions as "not authoritative."

Edwards came to Washington to carry out President Reagan's promise to shut the Energy Department down. While the legislation to do that isn't going anywhere on the Hill, it has to be assumed that his successor must promise to keep trying.

Broyhill is a cosponsor of that legislation in the House, but his aide said, "We don't think the department will be abolished anytime soon."