The incident happened at around 1.40pm on Saturday in a property on Liddesdale Road, Milton.
A 41-year-old was left with serious injuries after the pair entered his flat and attacked him.
He was taken by ambulance to hospital in Glasgow where medical staff describe his condition as stable.
The two men were spotted fleeing the scene to Scalpay Street before making a speedy getaway in a black Audi estate car, possibly along Balmore Road.
At around 2pm, a black Audi was found burnt out not too far away in the grounds of Lambhill Cemetery on Tresta Road.
Detective Chief Superintendent Kenny Graham, Govan CID, said: “At this time it has still to be established if this was the car involved. However, it does seem that it is the case.
“We need people to come forward with information about either the attack itself or who maybe saw the car being set alight or going in to the cemetery.
“Whilst we believe that this was a targeted attack and part of an ongoing feud in the north of the city, for men to be running about with knives, driving at speed along busy roads and burning a car in broad daylight in a busy residential area is contemptible with no regard for others that could have become involved or hurt.
“We are particularly keen to hear from drivers who were in the area and who may have any ‘dashcam’ footage of the two men or the Audi.
“If you have then please contact the CID at Govan Police Office via 101 quoting reference number 2106/24/06.
“If for any reason you do not want to speak to officers directly, then please contact Crimestoppers on 0800 555 111 where details can be given in confidence.”
The attempted murder suspects are described as being of average height and build, wearing dark clothing and masks.
Police are checking CCTV and speaking to people in the area to gather information.
The force is trying to establish if there was a third person in the car or whether the two men got in and drove off.
Additional officers have been deployed in the area and police said anyone with information or concerns can approach them.