It happened at the Shell petrol station on Altrincham Road in Baguley at about 00.45am on Monday 18 April 2011.
A man, his wife and their three-year-old son pulled up in their black Mercedes and the man went into the station.
While his wife and son were in the back the would-be thief opened the driver's door and got into the car.
The woman screamed and managed to get out of the car with her son, before her husband came out of the petrol station and ran towards the car, getting into the back seat as the offender tried to drive off.
The pair had a brief scuffle over control of the car, and after getting about 20m off the forecourt, the offender gave in, got out of the car and fled across Altrincham Road.
Police are now appealing to anyone who witnessed the attempted robbery to come forward.
The offender is described as:
- a white male
- aged in his 30s
- normal build
- small eyes
- 'boxer's nose'
- pock marks on his face and cheeks
- wearing a pale grey jumper with the hood pulled up and grey tracksuit bottoms
Detective Constable Dave Bigger, of West Didsbury CID, said:
"The offender clearly saw the opportunity to target a vulnerable woman with her young son, and subjected them to a great deal of distress in order to steal their car.
"However, realising his wife was in trouble her husband bravely struggled with the would-be thief in order to defend his family, causing the offender to give up and run off.
"But his intent was clear and whether he stole the car or not is immaterial - he put this family through the sort of ordeal no-one should have to go through and we need to find him and put him behind bars.
"I want to appeal to anyone who may have been either on the forecourt or inside the petrol station at this time and saw or heard what happened to come forward.
"Your information could be absolutely vital to us catching this man so we need to hear from you."
Anyone with information should call West Didsbury CID on 0161 856 6154.
Alternatively call Crimestoppers, anonymously, on 0800 555 111.