Venus, who is now assistant boss of Middlesbrough, had the items stolen from the house in Morningside sometime between midnight and 6am on Wednesday 29 December.
Both medals are about 12mm in circumference and not in their presentation boxes.
One is from the English Championship League season 2007-08 for West Bromwich Albion.
The other is from English Division 3 season 89-90 for Wolves.
A Lothian and Borders police spokesperson said: “These items are of tremendous sentimental value, so I would appeal to anyone with any information to get in touch so we can reunite them with their owner.
“They are very unusual, distinctive pieces so I would ask people to stay alert if they are offered for sale.”
