It cited "multiple current and former U.S. officials," who were not named.
Menendez said Friday that he had helped a family prosecuted by a "corrupt" government. He noted that the brothers entered the country in 2001 and had lived here legally ever since, under the Bush and Obama administrations. A Menendez spokeswoman said the U.S. government has rejected three extradition requests.
"My office had absolutely nothing to do with bringing these people here, giving them legal status, or refusing extradition orders," Menendez said. "Just because a corrupt Ecuadorean government declares these people to be fugitives doesn't mean that they are truly criminals."
"I am not aware of any official inquiry in this matter," Menendez said.
The brothers once led one of Ecuador's largest banks but were convicted of embezzlement after its collapse and fled to Florida.
Menendez said their bank was solvent until the government "ran it into the ground" and then blamed the Isaiases.
He sent four letters to the Department of Homeland Security in the spring of 2012 (one for each member of the family) urging the department to "fully consider" their applications for residency, Menendez spokeswoman Patricia Enright said.
Relatives of the two brothers donated more than $10,000 to Menendez's 2012 campaign, NBC reported, but Menendez said his actions were "standard inquiries."
"My office works with literally hundreds of individuals and families . . . from New Jersey and across the country who are seeking help with the immigration process. . . . We addressed this matter in an identical process," Menendez said. He later added, "We never, never act on a contribution as a cause for action."
Early last year, Menendez came under fire when news reports revealed that he accepted free flights on a donor's private plane and later wrote letters to federal agencies on behalf of the donor, South Florida eye doctor Salomon Melgen.
The "smear campaign" he referenced points to a report on the conservative website the Daily Caller, which cited an anonymous e-mailer's claims about Menendez's visiting prostitutes in the Dominican Republic.
Those allegations crumbled under scrutiny, and Menendez repaid the $58,500 cost of the flights, but his ties to Melgen remain under investigation, according to a December report by the Miami Herald. More than a year after the FBI raided Melgen's offices, no charges have been brought.