News of the possible sighting of Hazel North, from Cairneyhill, near Dunfermline in Fife, followed extensive searches for the 19-year-old at premises in Kilmarnock. The hunt failed to shed any light on her whereabouts.
On Tuesday, March 4, the teenager told her sister she was going to visit a male friend in the East Ayrshire town of Kilmarnock, nearly 60 miles from her home. She has not been heard from since.
However, officers last night said they were following up an apparent sighting of the teenager in Stranraer on Tuesday, March 18.
Police would not confirm who had reported the sighting, but said she was spotted around midday in Coronation Drive - a street which leads away from the town.
It is thought the teenager was in the company of another woman at the time, and officers are now appealing for her to come forward with any information that may help in finding the missing girl.
The woman is described as around 5ft 8in in height, of medium build, with short, dark hair in a bob style. She was wearing a dark coloured hooded top and dark blue jogging trousers.
Earlier, forensic teams carried out extensive searches in Kilmarnock, including at a flat and garden on Northcraig Road in the north of the town.
The house is one of four red brick flats within a social housing complex in the area.
Officers searched the premises, which locals said they thought were derelict, from around 6am on Friday and completed their search yesterday afternoon.
Police confirmed that they had not uncovered anything untoward, and said "extensive inquiries" were continuing in Dunfermline, Kilmarnock and Stranraer.
Officers are in the process of reviewing CCTV images in an effort to find out more information about the teenager's whereabouts.
Her family was said to have grown "increasingly concerned" for her and just want to know she is safe and well.
Superintendent Neil Kerr described the missing teen as a "vulnerable missing person", and said: "What I can tell you is we've carried out an extensive search of the house and the rear garden, as we would do with any missing person inquiry, but I can tell you at this time that we haven't uncovered anything that would give us any cause for concern at this stage."
He added: "We are currently following a number of lines of inquiry, speaking to family and friends to ascertain more information about Hazel and as to where she may be.
"Her family is obviously concerned by the lack of contact from her and they just want to know she is safe and well. If anyone has any information which could help us locate Hazel, please do contact us."
Kerr made a direct appeal to the young woman, saying: "Hazel, if you are out there, can you please get in touch with police as soon as you can and let us know that you are OK.
The missing teenager is described as 5ft 8in in height, and of slim build, with a fair complexion and shoulder-length blonde hair.
Anyone with information regarding Hazel's whereabouts, or who may have seen her since Tuesday March 4, is asked to contact Police Scotland on 101, or Kilmarnock Police Office on 01563 505000.