Suspicious packages have been seized in New York, Washington, D.C., Florida and California.
The sources said Sayoc had a criminal history and also had ties to NY.
An amateur body builder and former stripper who once spent time on probation for a bomb threat charge, Sayoc first registered as a Republican voter just ahead of the March 2016 Republican primary and quickly identified himself as a proud Trump supporter, tweeting and posting on Facebook videos that appear to show him at Trump rallies.
CNN has been a frequent target of Trump's "fake news" barbs, and a "CNN sucks" chant broke out at a Monday campaign rally. That package had an incorrect address, so it was redirected to Wasserman Schultz's office in Sunrise, Fla., and recovered there.
Homeland Security Director Kirstjen Nielsen, in an interview Thursday night with Fox News Channel, acknowledged that some of packages originated in Florida.
NY police are investigating another suspicious package which USA media reported was sent to a restaurant owned by actor Robert De Niro. Officials from the Bureau of Alcohol, Tobacco, Firearms and Explosives are at the sites of the multiple packages and were at Soros' Bedford, New York, home on Tuesday, a spokeswoman said.
The device sent to the Time Warner Center was a "live explosive device", NYPD Commissioner James O'Neill said at an afternoon news conference, adding that police were also investigating an envelope containing white powder that was found as part of the "original packaging" of the device.
Authorities also began investigating a suspicious package in Sacramento, California, addressed to Democratic Sen. The connection was being "strongly considered", said the federal law enforcement official, who would only speak on condition of anonymity because the investigations were ongoing.
Update: An earlier version of this report stated a suspicious package was intercepted on its way to the White House, based on CNN reporting. The address, 375 Greenwich St., matches that of the Tribeca Film Center.
Biden once said he would have fought Trump if they were in high school, while De Niro received a loud ovation when he hurled an obscenity at Trump at the Tony Awards in June.
The package was delivered by courier, law enforcement sources said.
Two packages addressed to Obama's former vice president Joe Biden were intercepted at a DE postal facility on Thursday.
The package was removed from the building around 7 a.m.
On Thursday evening, NY police sent the bomb squad to investigate two unattended packages at the Time Warner Center, where CNN's NY bureau was evacuated a day earlier after a pipe bomb was found in the mail room.
A federal law enforcement source told Reuters the devices were thought to have been fashioned from bomb-making designs widely available on the internet. At the time, they appeared not to know it was tied to the suspicious package sent to their building.
She is the former chairwoman of the Democratic National Committee who was accused by Clinton rivals of secretly helping the party's eventual presidential nominee.
Eric Holder, another prominent black Democrat, was attorney general in the last years of the Obama administration.
In addition, the NY offices of USA cable news channel CNN have been evacuated on Wednesday morning after a suspicious device was discovered in the building's mail room. And they came as authorities were intercepting more suspicious packages addressed to actor Robert De Niro, another vocal Trump critic, and former Vice President Joe Biden, who has also criticized Trump. The Secret Service said it had intercepted two bombs - one addressed to Clinton at the NY home she shares with former president Bill Clinton and another addressed to Obama in Washington that were found at mail screening facilities.
O'Neill and other officials were responding to questions about photos that have been circulated of the suspicious devices that led some experts to wonder whether the items pose a real threat or whether they were meant to be a scare.