Sgt. Diana McDaniel says the suspect called the non-emergency telephone number, but police were unable to trace the call.
The department is asking for help in identifying the man, as it cannot rule out that his threats weren't real.
McDaniel says the man is 29-years-old and wants to be called "Fleece Johnson."
His potential victim is a 26-year-old woman who lives five houses down on Columbia St. in New Westminster.
Police say the man claimed to have known the woman for five years, after meeting at a nearby pub.