The 26-year-old was in a car with family members about 4:30pm on Thursday when he was “targeted”, police said.
He got out of the car and was approached by two men before being shot at and missed.
He was then chased along Dykemuir Street in Springburn and attacked with weapons, leaving him with serious injuries.
The suspects, both of medium height and wearing dark clothing, fled in a blue 4x4 vehicle.
Their victim remains in hospital where staff described his condition as stable.
Detective Superintendent Kenny Graham said: “This was a violent and sustained attack which was carried out in the middle of a residential street in broad daylight.
“This is believed to have been a attack targeted at the victim and extensive inquiries are now under way to establish the full circumstances surrounding the incident and identify the individuals involved.
“I’m convinced there will have been plenty of people who witnessed this incident and it is absolutely vital that they come forward to assist us with the investigation.
“I would appeal to anyone who was in the area of Dykemuir Street yesterday around 4:30pm and may have witnessed what happened or heard any sort of disturbance to please come forward.
“I also suspect that the individuals involved may have been waiting for the victim in the area and I would ask anyone who noticed two men hanging around in the area prior to the incident, or anything at all out of the ordinary, to get in touch.
“Violence and people who would brandish a firearm in a busy residential street have absolutely no place in our communities.
“There is no doubt there are people who can help identify these individuals and bring them to justice.”