The report, citing the people familiar with the matter, however, asserted that the exchange's trading platform was not "compromised".
According to the US newspaper report, the federal investigators are trying to identify the perpetrators and are considering a range of possible motives, including unlawful financial gain, theft of trade secrets and a national-security threat designed to damage the exchange.
The report said it couldn't be determined which other parts of Nasdaq's computer network other than the trading platform were accessed by the hackers.
The Nasdaq situation has alerted the authorities because of the exchange's critical role, which officials put right up with power companies and air-traffic-control operations, all part of the nation's basic infrastructure, it added.
People familiar with the matter called the incident equivalent of someone sneaking into a house and walking around but—apparently, so far—not taking or tampering with anything.
The report said that Nasdaq declined to comment on the issue.
A probe into the matter was started by the Secret Service and now includes the Federal Bureau of Investigation.
The report said that although the authorities haven't yet been able to follow the trail to any specific individual or country, those familiar with the case said some evidence points towards Russia.
It, however, also mentioned that the person or people responsible could be almost anywhere, perhaps using computers in Russia merely as a conduit.
Preserving the stability and reliability of computerised trading, and ensuring that investors have full faith in that system are the two major concerns for the authorities, it noted.
In the past, Nasdaq's publicly accessible website was vandalised in 1999, when a group of hackers had claimed responsibility for defacing the site, as well as major media websites.
Nasdaq officials at that time said the company's internal network wasn't affected.