WASHINGTON — A few months ago, Senator Joseph I. Lieberman, an independent from Connecticut who is allied with the Democratic majority in the Senate, had a surprising guest at his office: Linda E. McMahon, the former wrestling mogul who is seeking the Republican nomination for Mr. Lieberman’s Senate seat, now that he is retiring.

For about an hour, Mr. Lieberman gave a private briefing of sorts on a range of topics, including national security, to Ms. McMahon, who would no doubt benefit from adding political heft to her résumé after a career at World Wrestling Entertainment.

“She’s bright and likeable,” Mr. Lieberman said in an interview.

Mr. Lieberman may not be running for re-election, but he is not content to fade away, it seems.

As candidates in both major parties begin jockeying for his seat, Mr. Lieberman has been doing and saying things that have confounded the political establishment — much as he has done in recent years.