"Buckle your seat belts!" said Rivera before announcing, on his radio show on WABC-AM in New York, that he is "truly contemplating" a Senate bid.
He said he has spoken to some people in the New Jersey GOP about a run, but he didn't say what they told him.
At 89, Lautenberg is the oldest sitting U.S. senator. The Democrat hasn't said if he will seek re-election.
Booker, also a Democrat, has announced he is exploring a run but hasn't made clear if he would challenge Lautenberg in a primary, should he seek another term.
No Republican has formally announced an interest in running.
Rivera, who is 69, said he has commitments to Fox and the radio show, but "I figure at my age if I'm going to do it, I gotta do it."
"And there doesn't seem to be any Republicans ready to work against or run against" Lautenberg or Booker, he said.
The New Jersey Republican party did not return an email asking for comment.