"I really do believe, as a modern Republican, that there is a point of view that is unrepresented in states like New Jersey," Rivera, a lawyer, said in an interview on Fox.
He called for a "new vitalization of the Republican Party" that highlights the "virtues of good business and fiscal policy," reining in entitlement programs and dealing with the national debt.
Rivera, 69, said he supported same-sex marriage, immigration reform and abortion rights.
Should he run, Rivera could face 89-year-old Sen. Frank Lautenberg, who has yet to say whether he is running for re-election in 2014, and Newark Mayor Cory Booker, 43, a Democrat who has announced for the seat.
Rivera said he has "been in touch with some people in the Republican Party in New Jersey," The (Newark, N.J.) Star-Ledger reported.
"Fasten your seat belt," he said.
2014: The Year in Music [PHOTOS]