The male and female officers tried to speak to people in a car in Banner Drive, Knightswood, at 23:15 on Sunday.
The car then reversed and struck both, leaving the 30-year-old female officer in intensive care.
Her 31-year-old male colleague also remains in hospital with serious injuries.
A blue Nissan Qashqai which had been at the scene was later found burned out in Lennox Gardens in the Scotstoun area of the city, although it has not yet been established whether it was vehicle used in the attack.
Det Insp Ian Hylands said: “Despite the damage, forensic officers will carry out a comprehensive examination of the car.
“Everything that can be done to locate the suspects is being done but I would like to appeal to anyone who may have seen the incident last night or who has any knowledge of the vehicle or the suspects to contact us.
“Two police officers, in responding to an incident to help protect the public, have been badly injured. Help us find those responsible.”