The men used the stolen car – a silver-colored Suzuki Celerio – to force their way into the main section of the mall around 2:50 a.m. before attempting to break into one of the shops inside.
After failing, they left the first car and drove off in another vehicle, a saloon-type silver car.
Both men have been described as slim and were wearing dark clothes, with their hoods up and covered.
Police investigations have established that Celerio had been stolen from the Stevenson Road area of Edinburgh on Tuesday night.
Officers are now seeking to determine the exact movements of the cars and the identities of the two men involved in the incident.
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Detective George Calder said: “Our investigations into this incident are ongoing and I would urge anyone who may be able to help to get in touch.
“We would be eager to speak with anyone who can help us determine the movements of the two vehicles involved or identify the two men seen at the Gyle Center.
“We will also be eager to speak with anyone who may have dashcam or private CCTV footage that may assist our investigation.”
If you have any information, call Police Scotland on 101 indicating incident number 0246 on 10 November or call Crimestoppers on 0800 555 111.