Officers said the 31-year-old victim, who has not been named, was stabbed in the chest during the assault on Saturday, June 19.
He was discovered, seriously injuried, on Balmore Road, close to Strachur Crescent at around 3am, according to detectives.
The man was taken to Glasgow Royal Infirmary by paramedics, where his injuries have been described as serious but not life-threatening.
The force has now appealed to the public for information, asking anyone in the local area at the time of the attack to come forward.
It also requested anyone who may have dashcam or private CCTV footage that can help them with their investigation to make contact.
Detective Constable Robert Carrigan, of Stewart Street Police Station, told reporters: "Our enquiries are ongoing into the incident and how this man came to be injured.
"Our enquiries so far suggest he was assaulted and I would urge anyone who may be able to help us to come forward.
"If you were in the area of Balmore Road in the early hours of Saturday morning and may have seen or heard a disturbance then please get in touch,” the detective urged.
“We would also be keen to speak to anyone who may have dashcam or private CCTV footage from the area.
He added: "Anyone with information can call 101, quoting incident 0717 of 19 June, or call Crimestoppers anonymously on 0800 555 111."