The man fled the scene, police believe without taking anything, the spokeswoman said.
"Police have been conducting enquiries this morning and the investigation is ongoing."
The elderly woman did not want to comment when contacted by the Herald.
"It's been quite a trauma for me and I don't want [to say] anything."
Her neighbours either didn't want to comment and or had not heard about the allegation.
The woman's son wrote on Facebook that neighbours were alerted after his mother yelled at the man. In a later comment he described the alleged weapon as a hand gun.
He praised police for their "fantastic and large" response, and said the man's description matched that of someone who had knocked on his mother's door the day before looking for someone. "Please please share this and beware of these people and behaviours."