The medals, three gold and one silver from four successive Olympics, were stolen from Oarsome Foursome rower Drew Ginn's car in Melbourne's Docklands.
Police confirmed on Wednesday afternoon they are looking for Luke Tones, 47, over the theft, with an arrest warrant issued for his capture.
The medals had been left in Ginn's car, on Cumberland Street, after he gave a talk at a school on Friday.
They were stolen between 9pm Thursday and 5am on Friday.
"They were hidden away in the car but the car was ransacked completely so lots of stuff was broken and destroyed," Ginn told ABC Radio on Wednesday.
The Olympic medals of former rower Drew Ginn (left) cannot be insured. (Dave Hunt/AAP PHOTOS)
The rower said it was hard to put a dollar value on the medals.
"They've got a lot of value for family and friends but you can't insure them," he said.
The legendary Oarsome Foursome was a series of Australian rowing coxless four crews, with Ginn taking part in latter combinations which won gold at the Atlanta 1996 and silver at London 2012.
He also won gold medals in pair events at Athens 2004 and Beijing 2008.
"There might be a market out there for this kind of thing but you'd hope sensibility would play out and in the end I know other medals have been returned in years gone by, so we hope that that happens in this case," Ginn said.
Detective Sergeant Timothy Reiher said the items were "unbelievably rare items with significant sentimental value".
"Olympic medals are awarded to the best of the best and are priceless to their recipients," Det Sgt Reiher said.
"We ask that people look out for these medals in pawn shops and online selling platforms."
Anyone with information on Tones, known to frequent Richmond, Abbotsford, Collingwood and Melbourne CBD, is urged to contact police.
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