Officers went to the resdential area in Gorebridge and traced the man to Cadwell Gardens, but did not find any weapon. Police said their enquiries were continuing.
A Police Scotland spokesperson said: "Around 3.30 pm a report was made to police about a man who was believed to be in possession of a weapon. Officers attended and the man was traced to Cadwell Gardens in Gorebridge. However, no weapon was found. Enquiries are continuing."