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8 year oldNew York, Texas and Virginia are believed to be the potential targets mentioned but a police spokesman said the information "lacks specificity".
Officials say they regularly assess all possible threats before major events.
Voters go to the polls on Tuesday to decide whether Donald Trump or Hillary Clinton will be the next president.
Both candidates are due to hold parties in New York after polls close on election day.
The FBI said that it was working closely with law enforcement agencies and sharing intelligence reports.
A spokesman for the Port Authority of New York, which operates airports, tunnels and bridges around in the city, said it was "continuing with the high level of patrols" it already had in place.
As well as preparing for the election, New York is also hosting the city's annual marathon on Sunday.
"The people of New York should feel safe," Police Commissioner James O'Neill told CNN. "We do large events in New York City like no other city."
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News of a possible attack came as both Mrs Clinton and Mr Trump made final pushes for support in battleground states across the US.
They both held rallies in Ohio and Pennsylvania, two states that may prove crucial on Tuesday.
Mr Trump is currently ahead in Ohio, according to a state polling average by Real Clear Politics, while Mrs Clinton leads by a small margin in Pennsylvania.
National polls have suggested that the Republican candidate has gained substantial ground on his rival in the last week or so. That momentum also appears to have helped him in several key battleground states.
The Democratic nominee has had a tough few days after the FBI said last week it was looking into emails that may be connected to her use of a private email server while she was secretary of state in the Obama administration.
Mrs Clinton has said she is confident the new inquiry will not change the FBI's original finding in July, which criticised her but cleared her of any illegal acts.
The Clinton camp have questioned the timing of the announcement and two senior Democrats have now called for an investigation into Trump surrogate and former mayor of New York Rudy Giuliani's role in it.
In an interview on Fox News on Friday morning, Mr Giuliani appeared to suggest he knew about the inquiry before it was announced, saying: "I had no role in it. Did I hear about it? You're darn right I heard about it."
Democratic Representatives Elijah Cummings and John Conyers wrote to the Justice Department on Friday afternoon asking for an investigate into the source of the information to Mr Giuliani.
"Leaking this information to former FBI officials as a conduit to the Trump campaign is equally intolerable," they wrote in the letter.
But Mr Giuliani later denied having prior knowledge of the inquiry, telling CNN he had not received advance notice from FBI: "No, I've spoken to no current FBI agents."
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