Ryan Sherry is thought to have been chased from a block of flats by a gang before he was attacked with a knife.
Officers believe he may have been involved in a disturbance before the attack, in the Springburn area of the city.
They have released a picture of the 21-year-old, who was from the local area.
Officers said they were following a definite line of inquiry, but have appealed for help from the public.
They want to speak to an elderly couple who were seen walking their dog around the time of the attack.
As reported in yesterday's Evening Times, the man was attacked in Petershill Road, Springburn, near the fire station, at about 10.30pm.
He died later in the city's Royal Infirmary.
Officers have been carrying out door-to-door inquiries and studying CCTV footage.
Almost a mile of Petershill Road, from Springburn Road to Auchinloch Street, was sealed off while they carried out their investigation.
Detective Superintendent Kenny Dewar said: "I am appealing to locals who may have seen or heard anything – and in particular the elderly man and woman who were out walking their dog.
"They may have seen something or have information which could assist our investigation. I am asking them please to get in touch."
Meanwhile, police are treating the death of a man found in a Lanarkshire park as unexplained.
The body was found by a dog walker in Souterhouse Park in Coatbridge on New Year's Day. It is thought the dead man – who was found at about 9.45am – was a Hogmanay reveller in his 20s.
Police said the death was being treated as unexplained until the results of a post mortem examination were known.