The Celtics and Bulls had extra security around their benches during Game 3 of the first-round playoff series to keep an eye on Allen. A source said the added security presence was a precautionary measure, according to the Globe.
Allen, who is from Chicago, played nine minutes on Thursday night and did not score in the team's 107-86 win against the Bulls.
Sources told the Globe that Allen has been receiving threats in Chicago for some time. Allen also was threatened prior to a March 17 game at Chicago. He didn't make that trip, however, because of a thumb injury.
"Is that what you're going to write about? Is that what you're going to write about?" Allen said when asked about the threats, then walked away, the Globe reported.
"It's a private team matter," Celtics president Rich Gotham told Yahoo! Sports. "It's just not something that we are going to talk about."
Celtics coach Doc Rivers told the Globe: "It's a team matter. We will keep it in house."
The NBA also declined comment to Yahoo! Sports.
In April 2007, Allen was found not guilty of aggravated battery in a Chicago court. That charge was connected to a fight in August 2005 outside a Chicago restaurant.