In a court filing, Tsarnaev's lawyers said they intend to file a change of venue motion, but they asked for more time to analyze media coverage of the case before filing the request.
The defense asked the judge to extend the deadline to file the motion from June 18 to Aug 3.
Authorities say Tsarnaev, then 19, and his brother, Tamerlan, 26, planted two pressure cooker bombs near the finish line of the 2013 marathon in an attack they saw as retaliation for U.S. wars in Muslim lands.
Dzhokhar Tsarnaev has pleaded not guilty to 30 federal charges and is awaiting a trial scheduled to begin in November. He faces the possibility of the death penalty.
Tamerlan Tsarnaev died following a shootout with police several days after the bombings.
Change of venue motions are rarely granted, with many judges opting to move ahead with jury selection and giving lawyers the chance to renew their requests if it proves difficult to find a fair and impartial jury.
However, judges have agreed to move trials in some other high-profile cases, including the trial of Oklahoma City bomber Timothy McVeigh, whose trial was moved from Oklahoma to U.S. District Court in Denver.
Christopher Dearborn, a professor at Boston's Suffolk University Law School, said Tsarnaev's lawyers could make an argument that the trial should be moved to U.S. District Court in Springfield, in western Massachusetts, where "the emotions wouldn't be quite as intense" as in Boston.
"It's really hard, I think, to say with a straight face that he is going to get a fair trial in Boston," Dearborn said.
"I'm not so sure this guy can get a fair trial anywhere. You can't try the case on Mars. It's a problem with really serious high-profile cases."
A spokeswoman for U.S. Attorney Carmen Ortiz declined to comment, saying prosecutors would file their response in court.