Comedian Michael Rapaport was also on the show and upon hearing this, exclaimed, "Whoa, whoa, whoa! Andy, don't let this go!"
Cohen then asked if she actually dated the 79-year-old actor, of which she replied, "Who hasn't? Don't forget how old I am and don't forget those days before cell phones-- those old answering machines."
"Did you have more than one night with him?" the late-night host further inquired. "Would you stop going into the lovers, the hookups? Nobody nails down Nicholson!" she answered, adding that the alleged fling was "one big sloppy mess" that occurred "whenever we could."
Morgan -- who once dated Prince Albert -- continued to play the game, and revealed who she would and wouldn't be willing to date. The 53-year-old reality star passed on the Dalai Lama, David Letterman, Vladimir Putin, Bill Gates. She also turned down Prince Charles because he was too "high profile."
When Cohen noted that Nicholson is pretty high profile, she said, "That was on the down low."
Morgan went on to respond to rumors that she once dated President Donald Trump, insisting that they've "always" been just friends. "I went to his wedding and his ex-wife Ivana's wedding," she said, referring to herself as a "friend of the family."