An attorney for Bulger argued a jury should resolve the question but the judge in the case, U.S. District Judge Richard Stearns, declined to decide the matter Wednesday, giving both sides 14 days to submit further arguments, The Boston Globe reported.
Bulger, 83, claims a former federal prosecutor -- Jeremiah O'Sullivan, who died in 2009 -- granted him immunity for all his crimes because he acted as an informant.
Prosecutors argued last week a recorded conversation Bulger had while in jail proves he was not an informant.
In the conversation with his brother John, recorded in September 2012, Bulger says: "I bought [expletive] information, I didn't sell it. I never gave them [expletive] information. Nothin'. Nothin'."
Bulger, who is charged with participating in 19 murders in the 1970s and '80s, was captured in Santa Monica, Calif., in June 2011 after being on the run for more than 16 years.
He fled Massachusetts just before being indicted in 1995, after he was tipped off by a now-imprisoned former FBI agent, John J. Connolly Jr.