"Investigators so far believe that Russian intelligence is likely behind the attacks and that Russian hackers are targeting news organizations as part of a broader series of hacks that also have focussed on Democratic Party organizations, the officials said," CNN said.
Reuters could not immediately confirm the report. The FBI declined to comment, and representatives for the US Secret Service, which has a role in protecting the country from cyber crime, did not immediately reply to a request for comment.
The intrusions were detected in recent months, according to CNN.
Citing the US officials, it said the Times had hired private security investigators to work with national security officials in assessing the breach.
Representatives for the Times could not be immediately reached for comment.
The Democratic National Committee, Democratic presidential candidate Hillary Clinton's campaign and the party's congressional fundraising committee have all been affected.
Hackers have also targeted the computer systems of Republican presidential candidate Donald Trump and Republican Party organizations, sources have told Reuters.
If confirmed, the breach at the Times would not be the first time foreign hackers infiltrated a news organisation: media are frequently targeted in an order to glean insights into US policies or to spy on journalists.
In 2013, a group of hackers known as the Syrian Electronic Army also attacked Times and other media outlets. Chinese attackers also infiltrated the Times that year.