In one case, authorities intercepted conversations among al Qaeda adherents overseas about targeting three different states -- New York, Texas and Virginia -- according to one local and one federal law enforcement official.
But the officials stressed that the threat is non-specific, could just be idle chatter and is not seen as imminent.
It is one of many security concerns authorities are monitoring in the run-up to Election Day.
New York law enforcement is already on heightened security with the city hosting a marathon this weekend that will attract huge crowds, voting on Tuesday, and both presidential candidates' Election Night campaign parties.
Officials said a great deal of security measures are in place.
"You can assume there will be considerable security around Election Night, particularly given, as I understand it, that the two major party candidates will be having events in New York City," Department of Homeland Security Secretary Jeh Johnson said Friday. "And so there will be considerable security contributions by the federal government, by the NYPD state and local law enforcement."
"We have these concerns around every election, but I have to say that I think there is more of a concern this time than I've seen in the past," California Rep. Adam Schiff, the top Democrat on the House intelligence committee, told CNN's Jake Tapper on "The Lead."
"There is a threat and I can't go into specifics," he said. "But we often see around pivotal events, like an election, like July 4, an increase in the threat to the country and here you have al Qaeda that is still trying to prove that it's lethal, still trying to compete with ISIS, ISIS losing its caliphate, trying to lash out."
More typical concerns about Election Day have also been compounded because of the particularly divisive campaign, according to law enforcement sources. That's led to concern among law enforcement officials about someone agitated by the toxic political environment taking criminal action.
CBS News was first to report the al Qaeda threat.
A New York police spokesman said the force is "aware of the information" and working with the FBI.
"We take any intelligence reports regarding New York City seriously," said J. Peter Donald, NYPD spokesman. "In this case, I would point out that the credibility of those reports is still being assessed and the information lacks specificity."
A law enforcement official in Texas told CNN that there is no specific and credible information that is suggesting a threat to elections in Texas. But the official added that authorities remain very vigilant throughout the state.
Texas Gov. Greg Abbott issued a statement noting that his office was working with law enforcement to monitor the situation.
"Texans should go about their daily lives as usual, but remain vigilant over the next several days and report any suspicious activity to state or local law enforcement," he said. "The State of Texas will continue to do everything it can to ensure the safety and security of its citizens."
Virginia State Police issued a statement Friday afternoon saying authorities continue "to assess any potential threats associated with the election or other major events taking place within the Commonwealth."
The statement noted that the police already have plans in place "to ensure the safety and wellbeing of our communities on Election Day."
Speaking at Newark Liberty International Airport, Johnson did not directly comment on the reports regarding Election Day security. Instead, he advocated his department's vigilance in reviewing all possible threats and related preventive procedures.
"I won't comment on the specific item in the news except to say, in a general manner, the American people need to know that the Department of Homeland Security, the FBI, state and local law enforcement review our security posture, review intelligence, review threat streams daily if not hourly," Johnson told reporters Friday. "Something I did this morning."
Federal authorities are also working with local officials across the country.
"The FBI, working with our federal, state and local counterparts, shares and assesses intelligence on a daily basis and will continue to work closely with law enforcement and intelligence community partners to identify and disrupt any potential threat to public safety," according to a statement from the FBI's New York field office.