Co-counsel J.W. Carney Jr. and Hank Brennan said they "seek only to defend [Bulger's] reputation and provide the public with a fuller, fairer understanding of this historic trial."
Bulger is on trial for charges of racketeering, participation in 19 killings, money laundering, illegal gun possession, and extorting drug dealers, bookmakers and businessmen.
His lawyers said reporters and columnists covering his trial -- which enters its ninth day Monday -- have villainized him.
"The overriding tenor of the media coverage has been adverse to the defendant. Prominent local newspapers have launched personal attacks against him on a regular basis," their motion to U.S. District Judge Denise J. Casper said.
Prosecutors said if Bulger wants to tell his side of the story, he should do so from the witness stand, the Boston Herald reported Sunday.
"He now complains that he has no 'voice' in the media if he is not allowed to have his attorneys give press conferences outside the courtroom in the midst of a trial," U.S. Attorney Brian Kelly said. "Bulger, who has five taxpayer-funded attorneys in the courtroom helping him find his 'voice,' can also exercise his actual voice from the witness stand if he so chooses -- subject of course to cross-examination."