In images obtained by the Daily Mail, Maisani is seen openly kissing and holding hands with an unknown man in a New York City park.
A source close to Cooper told The Huffington Post that the alleged affair is particularly hurtful, since the news anchor only publicly came out as gay last month.
"He never wanted to be the poster boy of the gay movement, but he has become that. This is all very sad," the insider said.
The source added that the couple may not be compatible in the long run, explaining: "They both have very busy lives and have enormous trust in each other. But at the end of the day, they come from very different worlds.
"Just this weekend, Anderson was hanging out with Beyoncé at the UN headquarters for World Humanitarian Day, while Ben runs a gay bar in the East Village."
Ellen DeGeneres and Kathy Griffin applauded Cooper's decision to come out following his announcement.