Officers were called to the scene at Edmiston Driven near to Paisley Road West just after 7pm, prior to the Rangers v Osijek game at Ibrox Stadium.
Two men, aged 24 and 40, were found injured and were taken by ambulance to the Queen Elizabeth University Hospital for treatment to stab wounds.
Medical staff describe their conditions as stable.
Detective Inspector Steven Wallace said: “This type of violent behaviour will not be tolerated and it is absolutely vital anyone with information that could assist with our investigation comes forward.
“I would appeal to anyone who was in the area and witnessed a disturbance, particularly anyone with mobile phone or dash-cam footage, to get in touch.
“Anyone with information is asked to contact Govan CID via 101. Alternatively you can call CRIMESTOPPERS on 0800 555 111 where details can be given in confidence.”