The 62-year-old Dobbs lives on a 300-acre farm in Sussex County in rural northwestern New Jersey.
Dobbs didn't respond to messages left Thursday at his home and office, but his assistant at CNN, Arlene Forman, said "He has no comment."
Dobbs issued similar sentiment to The Star-Ledger of Newark.
"I'm just not going to comment," he told the newspaper.
Several people earlier this year floated Dobbs' name as an independent presidential candidate, but Dobbs told the Wall Street Journal in January that he wasn't planning to run.
"I haven't got the personality or nature to be a politician," he said.
But he also added, "I cannot say never."
Dobbs was registered to vote in Sussex County as a Republican, but changed to an independent in 2006, according to the county elections board.
Tom Wilson, the state Republican Party chairman, said he's not taking the rumors seriously.
"At this point, it's nothing more than a whole bunch of rumors and speculation," Wilson said.
If Dobbs is thinking about running for governor as a GOP candidate, Wilson said he should start with registering as a Republican and talking to New Jersey Republicans.
"If he's interested, hey great, but you need to talk to people in New Jersey," Wilson said. "While he may be a known name, I think it takes a little more than just sitting in a news studio somewhere, saying, 'I think I want to be a candidate, all of you come running to me."'
Wilson said most Republicans want U.S. Attorney Christopher Christie to run for governor next year. Christie has built a reputation as a corruption-buster, but hasn't said whether he will run.
Democratic Gov. Jon S. Corzine, a former Goldman Sachs chairman who became a multimillionaire on Wall Street before entering politics, has said he intends to run for re-election next year.
"He'll be in a strong position for re-election no matter whom the Republicans nominate," said Rich McGrath, spokesman for the state Democrats. "But the other Republican candidates might want to get equal time on CNN if Mr. Dobbs runs."
