Stuart Lancaster's side have not beaten the Wallabies for three years heading into tomorrow's clash at Twickenham.
Woodward, who led England to victory in the 2003 World Cup, told Sky Sports News: "I really hope the scrum goes well. I hope it's not just a succession of penalties at scrum time. If England batter Australia at the scrum then they'll win.
"But if the Australians can compete in the scrum then we've got a great game of rugby, they're building a great side. But then so are England and I think some of the selections are really exciting.
"I think [Billy] Twelvetrees brings a lot and he'll help Owen Farrell. I really want England to go out and attack but I hope the game isn't won on penalties because England smash Australia in the scrum."
England will also face Argentina and New Zealand over the next month.