F1 boss Bernie Ecclestone told the Sunday Herald Sun that he wanted the race switched from the afternoon so it would fit in better with European television time zones.
Similar concerns may influence the timing of the recently announced Singapore Grand Prix.
"I would like to make sure we can watch (the race) in Europe and other parts of the world at a respectable time rather than having to get up at three or four in the morning," Ecclestone told the newspaper.
Australia has hosted a round of the Formula One championship every year since 1985. The event was initially staged in Adelaide but moved to Melbourne in 1996 and has been there ever since.
Melbourne has been the venue for a round of the championship since 1996 when the race moved from Adelaide.
Melbourne's current contract expires in 2010 and several countries are vying for its slot on the calendar.
"When the contract comes up, we have to have a look and see exactly what we will be doing with Melbourne," Ecclestone said.
"Unless they (organisers) can come up with something satisfactory, I'm pretty sure we wouldn't be able to continue there."
Australia could lose it Formula One Grand Prix unless it moves to an evening time slot, according to local press reports.
