Philippe Drice, 57, said he met the woman during the summer last year while she was eating with a friend at a Subway restaurant, the New York Daily News reported Wednesday.
Drice, who is Haitian, blamed racial issues for his failure to get the woman's last name or phone number during their encounter.
"As you can see, it's a biracial thing, and I guess we were both being careful," Drice said. "I think we were both being overly cautious."
Drice said he was smitten with the woman and wants to reconnect with her in time for Valentine's Day.
"She had those looks," Drice said. "Her whole demeanor was so fluid. Her tone of voice. Everything about her gave me an idea of a mermaid in my head."
"I lost a mermaid in downtown Brooklyn," Drice wrote on the dozens of flyers he has been putting up in areas including the neighborhood surrounding the subway. "Should you reunite us for Valentine's Day 2014 ... You collect a $100 reward."
Drice, who admitted his quest is "not normal" and "an act of total desperation," said he plans to make good on the offer.
"It's an incentive," Drice said of the promised $100 reward. "I'm a businessman. I'm not asking anyone to do anything for free."