Plagued by legal trouble and abandoned by his allies, Senator Robert Menendez has made clear what he will not do: quit before his term is over in January.

He has taken to the Senate floor to profess that he is innocent of what he insists are trumped-up bribery charges pursued by overzealous federal prosecutors. And he has ignored widespread, sometimes mocking calls for his resignation.

But when it comes to whether Mr. Menendez, a New Jersey Democrat, intends to seek re-election, he has been uncharacteristically coy.

“I don’t think announcing it in a courtroom would be the best idea,” he said after being arraigned Monday in Manhattan for the third time on charges that he participated in a yearslong bribery conspiracy.

The vacuum has been filled by a swirl of rumors in New Jersey and Washington, and contradictory news media reports. The New York Post, for example, reported last week that Mr. Menendez would not run for re-election. Then, on Thursday, NBC News wrote that he might still run — as a political independent.

Both cited information from anonymous sources that Mr. Menendez did not directly deny or confirm. “When I decide to declare whatever my path is, I will do it then,” he told NBC. On Friday, a spokesman for the senator declined to comment about his political intentions.