Bulger was 89 and serving a sentence of life in prison, and had recently been transferred to the high-security Hazelton penitentiary in West Virginia, according to NBC News.
Henry Brennan, a defense lawyer for Bulger, said in an email he could not confirm or deny the reports.
Officials at the Federal Bureau of Prisons did not immediately respond to requests for comment.
Bulger was convicted in August 2013 of 11 murders, among other charges including racketeering, and sentenced to two consecutive life terms plus five years.
Prison had been something Bulger had gone to great lengths to avoid – killing potential witnesses, cultivating corrupt lawmen and living as a fugitive for 16 years. It all ended when a tip from a former Icelandic beauty queen led to his capture in June 2011 in Santa Monica, California, where he was living with a long-time girlfriend.
Bulger and his Winter Hill gang had operated for more than two decades in the insular Irish-dominated South Boston neighborhood, engaging in loan sharking, gambling, extortion, drug dealing and murder. They did so with the tacit approval of an FBI agent who looked the other way when it came to Bulger’s crimes so that he would supply information on other gangsters.
Bulger, portrayed by Johnny Depp in a 2015 film “Black Mass,” was feared for his short temper and brutality. Prosecutors said he strangled two women with his hands and tortured a man for hours before shooting him in the head with a machine gun.