"Let me let you know this: The only way I'm not going to be Governor next year is at the ballot box, and the only way I'll be leaving office before is in a box," Paterson said.
"Actually, the more frustrated I get, the more I know I am going to be running," he added.
Paterson also said "I have not had any conversations about resigning, because I don't know why I would be resigning."
"There hasn't been one shred of evidence that any of these charges being made against me are true," the governor said.
Paterson, who is scheduled to sit down with CNN's Larry King on Thursday, said he's written a letter to the Times concerning the article. He said he was interviewed Tuesday by Times reporters, who did not indicate they had information that would force him to resign.
Rumors about the governor have centered on speculation about adultery and drug use, but Paterson suggested those topics would not be the focus of the Times story.
"The article will be written about other subjects and not the ones that have been the source of mass speculation," he said.
He called the rumors "false allegations, unsubstantiated rumors, and, in some cases, straight-out lies."