The English club are owned by Eleonora Sport Limited but banned president Massimo Cellino has sold his personal stake in both the company and Leeds.
BBC Sport has learned New Zealand-born Crowe, who is a Leeds supporter, would consider buying the club if he was approached and had the backing of fans.
Leeds are currently 14th in the table.
Crowe, 50, is already the co-owner of rugby league club South Sydney Rabbitohs, who play in Australia's National Rugby League.
His affection for Leeds dates back to his schooldays, when he used to watch editions of the BBC's Match of the Day.
The reaction from Leeds fans was overwhelmingly positive.
Leeds Fans LLP, a group supporting fan ownership of the Championship club, told Crowe they wanted a "fan voice on the board" and they "would love to have" him involved.
That prompted Crowe, who has an estimated net worth of $75m (£48m), to lay out his management "vision".
"There has to be one voice that sets the tone," he wrote. "Every thought and every decision has to be about success on the field."
Leeds told BBC Sport they had not received an approach from Crowe.