"I like our chances against anybody -- anybody," Hurd said in an interview with CNBC at the OpenWorld conference on Tuesday. "I think we're going to win, bar none."
The numbers aren't in his favor. According to Synergy Research Group, Oracle isn't among the top four contenders, a group that includes Amazon, Microsoft, IBM and Google. The fourth-ranked cloud, Google, has just 5 percent of the market, while AWS controls 34 percent.
Companies can use public cloud infrastructure to run applications and websites. The market has become so competitive that vendors like Hewlett Packard Enterprise and VMware have ditched their public clouds. That's not in Oracle's plans.
Still, when asked if Oracle would crack the top three, Hurd wouldn't say.
"I'm not as riveted on whether it's six months, a year, 18 months -- because we're in this for the long haul," he said. "It's not as important to me about what the date is that we get to the destination, but what's more important to me is that we make progress every single day, and every single day we're better than we were yesterday."
Ambitious rhetoric is nothing new for Oracle leadership. Larry Ellison, the company's billionaire founder, has routinely said Oracle is beating rivals Salesforce and Workday in cloud software, despite what the results show.