The cap was bought by one Tim Serisier after he won 250,000 dollars in reality show 'Who Wants To Be A Millionaire'.
Serisier now wants to auction the cap and though auctioneer Charles Leski says a better timing could have fetched a higher price, the piece of memorabilia can still invite a hefty bid in the range of 600,000 to 750,000 dollars.
"I defy anybody to tell me anything in Australian sport that is more important or has a higher status," Leski was quoted as saying by 'The Sydney Morning Herald'.
"This is the single most valuable item we've ever auctioned - sporting, Australian, across the board," he added.
The auctioneer's confidence stems from the fact that a Bradman bat was recently sold for a world-record price of 145,000 dollars.
The cap comes with a memo signed by Bradman in 1996 declaring that "on his twelfth birthday I gave Richard Robins one of my Aust. XI caps".
Richard Robins' father, Walter, played 19 Tests for England and was Bradman's "best pal in the cricket world."