Australian newspaper The Daily Telegraph claims the Cinderella Man star announced the happy news at a dinner with record company executives in Melbourne last week.
Crowe and Spencer wed in April 2003 and the singer/actress gave birth to their son Charles in December 2003.
When asked for a confirmation or denial of the reports, Crowe's Australian management gave a "no comment."
Spencer was absent from the Australian Film Industry Awards (AFIAs) last month, where Crowe played host.
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