"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.
Hurd's latest comments come a few weeks after Oracle tied certain executive compensation to cloud growth goals. One goal is for Oracle to capture more than $10 billion in revenue from cloud platform and infrastructure services in a single fiscal year.
In the most recent quarter, Oracle's cloud infrastructure and platform services produced $400 million in revenue, up 28 percent year over year. Meanwhile, in the second quarter AWS generated $4.1 billion in revenue, up 42 percent from the prior year.
Oracle still has a massive legacy business. Hurd said he tells customers that the company isn't about to kill its software products that run in traditional data centers, so clients are not pressured to rush to the cloud.
"You have to move to the cloud, you have to move by June -- I don't think so," Hurd said.
That position, which to some degree mirrors Microsoft's, makes sense for Oracle. But the growth is, generally, in the cloud.
Just look at Oracle's results: The company generated less revenue in fiscal 2017 than it did three years earlier.