Bulger was moved to a West Virginia prison on Tuesday morning.
Bulger had been serving a life sentence after being convicted in 2013 in a sweeping racketeering indictment, including on counts of participating in 11 murders in the 1970s and 1980s. The Globe report was attributed to three sources briefed on the situation who spoke on condition of anonymity.
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The 89-year-old Bulger had recently been moved from a prison in Florida to a transfer facility in Oklahoma City. Bulger, who was 89, was found dead shortly after being transferred.
As Radar previously reported, the former Boston-based crime boss was finally captured in 2011, after more than 16 years on the run.
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Bulger was the head of the Winter Hill Gang, a violent South Boston crime ring, from the 1970 into the '90s. The Oklahoma facility he was held in last week often serves as a temporary stop for inmates in transit. Bulger became one of Flemmi's key allies during his time in the criminal underworld.
Bulger was arrested with his girlfriend, Catherine Greig.
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Bowers was also charged under state law with criminal homicide, aggravated assault and ethnic intimidation. Authorities say he expressed hatred toward Jews during the rampage and in later comments to police.
Bulger's life was portrayed in the movie "Black Mass", starring Depp. She also pleaded guilty to criminal contempt in 2016 for refusing to cooperate with authorities.