"You ever see a picture of her back then? Whew," the newspaper quotes John Spencer as saying of Clinton's appearance as a young woman.
"I don't know why Bill [Clinton] married her," Spencer added, according to the News.
The newspaper said Spencer attributed her improved appearance to "millions of dollars" in plastic surgery.
Spencer denied the News' story.
"It's a fabrication. I would never call Hillary Clinton ugly," he told the Associated Press. "That's outrageous. I didn't do it."
Separately, a Clinton spokesman denied that the senator had undergone any plastic surgery.
"Sadly, this is just the latest in a long line of insulting and offensive comments that John Spencer has made throughout his career, and it's unfortunate that he has chosen to run a campaign based on personal attacks," the spokesman said.
The Daily News said Spencer made the remarks on Friday during a plane flight to Rochester, the site of a debate between Clinton and Spencer. Spencer trails the Democratic incumbent by a wide margin in the polls.
On Monday, Clinton
"I've never seen a campaign where we're down to false accusations about appearance,'' she told reporters. "It's kind of a sad commentary."