It was not immediately clear what charges the suspect would face in the federal case but they would be in addition to the New York state murder indictment, the report late on Wednesday said, citing people familiar with the matter.
Federal charges would potentially allow prosecutors to pursue the death penalty, which has been outlawed in New York for decades, it said.
The US Department of Justice did not immediately respond to request for comment.
In the state case against him, Mangione, 26, has been indicted on 11 counts, including first-degree murder and murder as a crime of terrorism.
He would face a mandatory sentence of life in prison without the possibility of parole if convicted on all of those counts.
Ivy League-educated Mangione was charged with murder on December 9 for the killing of Thompson outside a Manhattan hotel before a company conference, following a five-day manhunt.
The killing of Thompson has ignited an outpouring of anger from Americans struggling to receive and pay for medical care.
Mangione suffered from chronic back pain that affected his daily life, according to friends and social media posts, though it is unclear whether his own health played a role in the shooting.
