The claims come as more and more allegations have been presented claiming that Cuomo has been bullying and inappropriately treating women, leading many both in the Republican Party and among Democrats to demand that he resign.
Shnayerson claimed that "abusive bullying" was part of the reason for the end of their marriage, according to the Post. He explained that a source close to the then-couple told him that she was "done being ridiculed and belittled."
Once Kennedy had filed for divorce, according to the report, Cuomo refused to move out of their house or to respond to her lawyers. This went on for half a year.
Seven women have openly accused Cuomo of sexual misconduct so far.
Chuck Schumer (D-New York), the Jewish Senate majority leader, joined others in calling on the three-term Democratic governor to resign.
Cuomo, 63, the divorced father of three daughters in their 20s, again repeated his denial of the allegations on Friday and said it was "reckless and dangerous" for politicians to ask him to resign before they have all the facts.
"Women have a right to come forward and be heard, and I encourage that fully. But I also want to be clear: there is still a question of the truth. I did not do what has been alleged: period," Cuomo said on a call with reporters.
"Wait for the facts. An opinion without facts is irresponsible," he said.
Asked on Friday if he ever had consensual romantic relationships with any of the women, Cuomo responded by saying only that he never intended to make anyone feel uncomfortable, and was sorry if he did.
A growing list of women, including former aides, have accused the governor of sexual misconduct, ranging from unwelcome flirtatious behavior at work to groping.
The new calls for Cuomo to resign came a day after more than 55 Democratic New York state lawmakers urged him to step down, and the state legislature said it would open an impeachment investigation into the allegations.
Reuters contributed to this report.