The report quotes people familiar with the saga as saying that the hackers made multiple incursions into the computer systems, and law enforcement officials are looking at several possible motives, ranging from a financial motive all the way through to planning an attack on the stock exchange at a future date.
The WSJ says that the probe into the hacking of the NASDAQ OMX system was started at the behest of the US Secret Service and now includes staff from the FBI.
The paper adds that, to date, investigators have been unable to track the hacking to any specific individual or country.
"So far, [the perpetrators] appear to have just been looking around", one person involved in the matter told the paper.
The WSJ adds that another person familiar with the case said the incidents were, for a computer network, the equivalent of someone sneaking into a house and walking around but apparently, so far, not taking or tampering with anything.
Infosecurity notes that the NASDAQ computer systems falls into the category of being part of the US national electronic infrastructure and any hacking event would almost certainly have triggered an investigation by the Department of Homeland Security.
The WSJ quotes Tom Kellermann, a former computer security official at the World Bank - now Core Security - as saying that said the most advanced hackers in the world are increasingly targeting financial institutions, particularly those involved in trading.
"Many sophisticated hackers don't immediately try to monetise the situation; they oftentimes do what's called local information gathering, almost like collecting intelligence, to ascertain what would be the best way in the long term to monetise their presence", he told the paper.
Whilst NASDAQ officials are not commenting on the reports, a spokesperson for the NYSE Euronext exchange, told the paper that his company takes any potential threat seriously.
"We are continually working to ensure that our systems operate at the highest levels of security and integrity", he said, adding that he declined to comment on specific hacking incidents.
This isn't the first time that NASDAQ's computer systems have been the successful target of hackers, as way back in the late 1990s, the exchange's external website was defaced by a group called the United Loan Gunmen.
NASDAQ officials said at the time there was no evidence that the hackers any manipulated financial data.