A number of sources tell Eyewitness News, Mr. Giuliani appears to be leaning toward a Senate run.
This could set up a blockbuster race for next fall.
Republicans have been watching polls showing that Giuliani would beat Democratic Senator Kirsten Gillibrand.
The polls also show that Giuliani would lose in a run for governor to the popular attorney general, Andrew Cuomo.
A spokeswoman for the former New York City mayor insists he still hasn't made up his mind about running for governor and won't be shy to say so when he does.
Spokeswoman Maria Comella disputed a New York Times report that Giuliani won't run for governor after months of considering it. The Times is citing unidentified people told of the decision.
"Rudy has a history of making up his own mind and has no problem speaking it. When Mayor Giuliani makes a decision about serving in public office, he will inform New Yorkers on his own," said Comella.
A Republican adviser says Giulani is expected to give Rick Lazio, the only announced Republican in the race, early notice of his decision. The adviser wasn't authorized to speak for the party and spoke on the condition of anonymity.
Lazio spokesman Barney Keller says Giuliani hasn't told them either way.
