Police were called to a property in Colston Road in the Springburn area at around 4.30am on Saturday after a disturbance.
Officers found three people injured - two men aged 39 and 44 and a 41-year-old woman.
All three were taken by ambulance to Glasgow Royal Infirmary.
The 39-year-old man is said to be in a critical but stable condition. The attack on him is being treated as attempted murder.
The other two injured parties are in a stable condition.
Investigations are continuing and it is understood police are following a positive line of inquiry.