Police Scotland have said officers have "no authority" to arrest a suspect who is the subject of an Interpol alert.
Harris Binotti is being sought by the authorities in Myanmar. They want to question him about the death of another British man, Gary Ferguson, in Yangon.
Both men had been working as teachers there. Mr Binotti left Myanmar the day before Mr Ferguson's body was found.
According to the Sun newspaper, Mr Binotti has been living openly in Glasgow.
Last week, Interpol issued a "red notice" - an international alert for a wanted person - for the Scottish teacher over the murder of his colleague.
However, the notice is not an official arrest warrant and cannot be used on its own by UK police to detain someone.
A statement from Police Scotland said: "The Myanmar authorities have the lead in the investigation into the death of Peter Gary Ferguson.
"Police Scotland has no authority to arrest anyone at this stage.
"Police Scotland will continually monitor any ongoing risk and take all appropriate measures."
It is understood UK authorities in Yangon are in contact with the Burmese police and have raised the case with senior officials at the Burmese Ministry of Foreign Affairs.
Contact has also been made with the Burmese Embassy in London to move the case forward.
The Interpol notice states that Mr Binotti faces a charge of murder and describes him as having brown hair and blue eyes and measuring about 1.68m (5ft 5in) tall.
Mr Binotti, who is from Dumfries, reportedly took a flight from Myanmar to Thailand before Mr Ferguson's body was found in his flat.
Mr Ferguson and the 26-year-old accused are believed to have gone out drinking two nights before his body was discovered and neighbours reported hearing sounds of a fight.
Both men taught English at the Horizon International School in Yangon, in the south of the country formerly known as Burma.
Mr Ferguson, who had a four-year-old son, had worked there for a year while Mr Binotti had been there for three months.
A spokesman for Interpol said: "At the request of Myanmar authorities, Interpol issued a red notice, or international wanted persons alert, for Mr Binotti.
"A red notice is a request to provisionally arrest an individual pending extradition issued upon the request of a member country based on a valid national arrest warrant.
"It is not an international arrest warrant."
Interpol said it did not arrest individuals, but added: "Many of Interpol's member countries, however, consider a red notice a valid request for provisional arrest."
A Foreign Office spokeswoman said last week: "We continue to do all we can to help and support the family of Mr Ferguson at this difficult time.
"We are in contact with the Burmese authorities responsible for the investigation."