While the companies are in exclusive talks, they could still fail to reach an agreement, the report said.
Micros shares spiked more than 15 percent on the Nasdaq. Oracle shares gained nearly 1 percent.
Micros Systems makes point-of-sale hardware and software for restaurants and hotels.
Oracle declined to comment, while Micros could not be immediately reached for comment.
FBR Capital Markets analyst Daniel Ives said Oracle's rivals could offer a higher bid to drive up the price.
Oracle has been rolling out its own cloud-based products and acquiring smaller cloud companies such as marketing software maker Responsys.
Smaller, aggressive companies like Salesforce.com and Workday have often undercut Oracle's pricing with competitive software and Internet-based products.
Four-decade-old Oracle's strategy is to integrate software with its own high-end, expensive hardware for greater efficiency.
Oracle reported quarterly revenue and profit that failed to satisfy investors looking for signs of a sustained turnaround and forecast in-line current-quarter results in March. The company is expected to report fourth-quarter results on June 19.
The deal, if confirmed, would be Oracle's largest acquisition since it bought Sun Microsystems for $5.6 billion in 2009.