Former U.S. senator William D. Hathaway and U.S. Ambassador to Canada Kenneth M. Curtis are the two names most prominently mentioned to succeed Sen. Edmund S. Muskie (D-Maine), who was nominated today by President Carter to be secretary of state.

Gov. Joseph E. Brennan has the power under state law to appoint Muskie's successor. No legislative confirmation is needed.

Had the vacancy occurred more than 60 days before Maine's primary election, which this year is June 10, state law would have required that Muskie's seat be filled by election.

Each of the major parties would have been required to nominate a candidate, and the primary winners would have faced off in the November general election.

Because fewer than 60 days remain before the primary, Brennan's choice will serve the remainder of Muskie's term, which ends in 1982.

Brennan said he would not appoint himself to fill the vacancy.

"I would consider that unseemly, number one," Brennan said. "Number two, I ran for governor to serve four years and I intend to serve four years to carry out my programs."

Brennan said he and Muskie met for about an hour this morning at the Naval Air Station at Brunswick, Maine, and discussed possible successors, but he declined to mention any names.

There has been a coolness between Hathaway and Brennan dating back to the last election, when Democrat Hathaway was defeated for reelection by Republican William S. Cohen, while Brennan was victorious. Many in Hathaway's camp complained that the Brennan staff was uncooperative and in some cases hostile to the Hathaway candidacy.

However, Hathaway has been a staunch supporter of Sen. Edward M. Kennedy (D-Mass.) in the Democratic presidential campaign, and Brennan was the first governor in the nation to support Kennedy.

Hathaway, who practices law in Washington, has said he was thinking of returning to public office and might seek to replace Muskie in 1982 if Muskie decided to bow out.