The Australian, irritated at local overregulation such as the prevalence of speeding and parking fines, made the comment in the wake of Lewis Hamilton's famous run-in with Melbourne police in March.
Then, when the formula one circus had moved on to Malaysia, Webber's father Alan and manager/partner Ann Neal posed with a group of fans wearing T-shirts bearing the words 'Victoria The Nanny State!'
One newspaper reader wrote at the time: "So this is the message from Mark Webber to the families who have lost loved ones on the roads this Easter. What a bloody disgrace."
Another added: "Don't come back Webbers. You are not welcome in my state."
The local Herald Sun newspaper said 33-year-old Webber's management has now written a letter to the government offering to have the Red Bull driver front a road safety campaign.
"It's something Mark is passionate about," Neal said. "It's not a knee-jerk reaction to the press he's had, it's something he has always done."
A government spokesman said Webber's offer was being considered.