A second source also briefed on the investigation said the driver, William Rockefeller, 46, lapsed into a "highway hypnosis."
The seven-car Metro-North train was traveling at 132kph, nearly three times the 48kph speed limit for the curved section of track where it crashed, investigators have said. The brakes were applied just seconds before it derailed.
The crash also critically injured 11 people and snarled travel for the roughly 26,000 regular commuters on the Metro-North Hudson line which serves suburbs north of New York City.
The National Transportation Safety Board (NTSB) has cautioned that its investigation would continue for weeks, if not months, and it was far from reaching a conclusion on the cause.
Rockefeller, who has never been disciplined for job performance as train driver, has retained a defense lawyer, Jeffrey Chartier, who did not immediately respond to a Reuters request for comment.
Rockefeller was due to meet with NTSB officials soon, according to the second source.
Rockefeller told investigators the train was operating normally when he somehow slipped into a daze, said the law-enforcement source, who has access to official reports on the investigation and requested anonymity.
Rockefeller told investigators he could not fully recall what happened, but that at some point he suddenly came out of the temporary daze, realised the train was going too fast and into a dangerous curve, and applied the brakes. It was too late to avoid the crash.
Law-enforcement agencies including the Bronx district attorney, the New York Police Department and transit police are monitoring the investigation.
If criminal charges are warranted, they would be brought by Bronx District Attorney Robert Johnson, a spokesman for Johnson said.
Asked whether Rockefeller dozed off, the second source said: "It's more like a highway hypnosis. You're looking straight ahead and you're seeing rail and rail and rail, and you lose perspective."
The train's throttle was reduced to idle six seconds before derailing and its brakes were activated five seconds before the accident, NTSB member Earl Weener told a news conference on Monday.
"He's very traumatised," Anthony Bottalico, the general chairman of the driver's labor union, the Association of Commuter Rail Employees, said. "He's devastated by the loss of life, by the injuries to the passengers and his fellow crew members, and he's extremely upset about all of it."
New York Governor Andrew Cuomo ordered the Metropolitan Transportation Authority, which runs Metro-North, to implement safety briefings for all employees, and Connecticut Governor Dannel Malloy asked Metro-North to provide an action plan on safety following the accident. Many Metro-North riders live in Connecticut and commute to New York City.
New York City Mayor Michael Bloomberg said better training and equipment were needed but that it required money that the state legislature was unwilling to spend.
"That requires money, and it's got to come from someplace. And so everybody's opposed to higher fares or raising taxes, which are the only things that you can really find money to improve services," Bloomberg told reporters.
"We did come up with a plan for more money for Metro-North and the subways and the buses in the city and it was rejected by the state legislature."
