American Chynna Deese, 24, and Australian Lucas Fowler, 23, were shot dead in British Columbia last week.
On Monday, the Royal Canadian Mounted Police (RCMP) released a composite of a man they want to speak to.
Witnesses saw him speaking to Fowler by the road where they were later found.
Police have not described the man as a suspect in the case.
What happened to the couple?
They were on a two-week-long road trip across Canada, where Lucas Fowler had been working.
The couple were found shot dead on the side of the Alaska highway 20km (12 miles) south of Liard Hot Springs – a popular tourist spot.
Police believe their murder occurred between 16:00 local time (23:00 GMT) on 14 July and 07:00 the next morning.
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Their 1986 blue Chevrolet minivan was found near their bodies, and eyewitnesses told media they had earlier seen the pair on the side of the road when their van had broken down.
It took three days for police to identify the couple.
Lucas Fowler’s father, Stephen, described the murder of his son and his girlfriend as “a love story that ended tragically” on Monday.
The young couple met at a hostel in Croatia in 2017, and had travelled the world together since.
“Our son Lucas was having the time of his life travelling the world. He met a beautiful young lady and they teamed up, they were a great pair and they fell in love,” he said.
Fowler’s father is a senior member of the New South Wales Police Force and has travelled to Canada with two other officers acting as family liaisons during the RCMP investigation.
Stephen Fowler says they will not get involved in the case directly.
“I’m an experienced police officer and I know how these investigations can go,” he said. “But I can tell you I am more than confident in all of the officers that are working on this case.”
What is the other case?
Police are considering the possibility the couple’s murder may be connected to the disappearance of two teenagers last Friday.
Kam McLeod, 19, and Bryer Schmegelsky, 18, are still considered missing.
They had been on their way to Yukon territory for work last week and have not been in contact with their families since.
Their burnt-out camper van was found along the side of the road near Dease Lake on Friday, almost 500km away from where Fowler and Deese were found.
A body was found burned not far from Kam McLeod and Bryer Schmegelsky’s van. It has not been identified but police believe he was a man in his 50s or 60s.
“It is unclear at this time how this deceased male might be connected with [the] vehicle fire or the two missing men,” police said in a statement.
On Monday, officials acknowledged the “growing community concern” about the twin murder investigations, after earlier dismissing a link.
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“It’s unusual to have two major investigations of this nature going on at the same time in northern B.C. (British Columbia), so we recognise the possibility that these could be linked,” Janelle Shoihet, public relations officer for the RCMP said.
Police are asking anyone with any information about either case to call Crimestoppers at 001-800-222-8477.