"We'll see what happens, I'm not even thinking about it right now," he said.

The Senator was asked multiple times about a potential future run and each time dodged the question, offering only that he's currently occupied with transitioning his responsibilities over to Senator-elect Elizabeth WarrenElizabeth Ann WarrenOvernight Regulation: Net neutrality supporters predict tough court battle | Watchdog to investigate EPA chief's meeting with industry group | Ex-Volkswagen exec gets 7 years for emissions cheating Overnight Tech: Net neutrality supporters predict tough court fight | Warren backs bid to block AT&T, Time Warner merger | NC county refuses to pay ransom to hackers Avalanche of Democratic senators say Franken should resign MORE.

"First of all, it is speculation, there's no vacancy that i'm aware of, and my biggest job right now is to make sure that there's a smooth transition from my office to the Senator-Elect's office," he said.

Kerry's name has been floated as a potential pick for Secretary of State or Defense, and if he were to take either position, a special election would take place for his seat.

Though Brown declined to offer any further details on his future plans, he did give hints during his concession seat that he may consider another run, telling supporters on election night that "defeat is only temporary."