The Democratic governor is already accused of sexually harassing two women and unwanted advances against him by a third.
CNN has reached out to Liss for comment.
"I never touched anyone inappropriately. I never touched anyone inappropriately," Cuomo said in his initial public comments on the scandal. "I never knew at that moment that I made anyone feel uncomfortable. I never knew at that time that I made anyone feel uncomfortable."
Cuomo said during an appearance on Wednesday that he learned from his behavior.
"I understand that sensitivity has changed, and behavior has changed, and I get it. And I will learn from it," he said.
Liss served as policy and operations assistant for Cuomo from 2013 to 2015, according to the Journal.
Liss originally thought of Cuomo's actions as "harmless flirtations", but she began to see them as "condescending", according to the Journal.
"It's not really appropriate in any setting," she told the Journal. .
One such incident occurred while Liss was working at the front desk of the Executive Mansion in Albany, New York, on May 6, 2014, according to the magazine.
"He came straight to me and he was like, 'Hey, honey! "" said Liss.
She told the magazine that "the governor hugged her, kissed her on both cheeks and then wrapped her arm around her lower back and grabbed her waist."
A photo shown by the Journal shows Cuomo & # 39 ;s hand around Liss & # 39; waist.
In response to Liss's claims, Rich Azzopardi, Cuomo's senior adviser, said in a statement to CNN: "Journalists and photographers have covered the governor for 14 years watching him kiss men and women and pose for pictures. there are hundreds of people, and he poses for hundreds of pictures. That's what people in politics do. "
Liss said she never made a formal complaint about the governor's behavior, but later asked to be transferred to another office. Liss said the experience led her to seek mental health counseling in 2014, according to the Journal.