"Thousands may be tied to Clinton's server," according to the Wall Street Journal.
It added that "metadata" on Anthony Weiner's laptop had suggested there was a connection.
The Journal reported that a review lasting "weeks" would examine the emails' content, whether they were duplicates of messages already seen by the FBI, and whether they contained classified information.
Mr Weiner is the estranged husband of one of Hillary Clinton's top aides, Huma Abedin.
He stepped down from Congress in 2011 amid a sexting scandal.
Hillary Clinton emails: Timeline of how scandal unfolded
A new investigation into Mrs Clinton's emails came to light in recent days.
FBI director James Comey has said it will examine whether the messages contain sensitive government information.
In July, Mr Comey said that Mrs Clinton had been "extremely careless" in handling classified information while Secretary of State, and that scores of emails on her server contained highly classified information.
But the FBI did not recommend criminal charges.
Top Democrats have demanded the FBI release "more detailed information" about its new investigation.
Senators Thomas Carper, Patrick Leahy, Dianne Feinstein and Benjamin Cardin have written a letter to Mr Comey and given him a deadline of Monday to respond.
The senators said: "This letter is troubling because it is vaguely worded and leaves so many questions unanswered.
"It is not clear whether the emails identified by the FBI are even in the custody of the FBI, whether any of the emails have already been reviewed, whether Secretary Clinton sent or received them, or whether they even have any significance to the FBI's previous investigation.
"The letter is also troubling because it breaks with the long-standing tradition of Department of Justice and the FBI exercising extreme caution in the days leading up to an election, so as not to unfairly influence the results."
Hillary Clinton has herself called on Mr Comey to put out the "full and complete facts" about the fresh FBI review.
Matthew Miller, a former chief spokesman for the US Department of Justice accused Mr Comey of making a "huge blunder" in his handling of the probe.
On Sunday, meanwhile, Mrs Clinton came out fighting at a rally in Florida.
While not directly referencing the investigation, she told supporters: "When you're knocked down what matters is whether you get up again.
"I'm not stopping now."
Mrs Clinton also attacked Donald Trump at Sunday's rally, calling him a "downer" who had alienated half the American population.
Meanwhile in Las Vegas, Mr Trump was also taking aim at his rival, accusing Mrs Clinton of corruption and telling the crowd that the only way to stop her was the "power of the vote".