Benjamin Brafman wrote in an e-mail to the AP that Burress will turn himself in Monday morning. Brafman said Burress "will enter a plea of not guilty."
Burress retained Brafman, a New York defense attorney, after the ninth-year veteran accidentally shot himself in the thigh Friday night at a Manhattan night club.
"I do not expect that Mr. Burress will make a statement," Brafman wrote.
He met with Burress for about an hour Sunday at the player's home in New Jersey.
"I would ask that his fans, the Giants and the media withhold judgment in this matter until all of the facts have been disclosed," Brafman wrote to the AP.
Brafman is a well-known criminal lawyer who has defended mobsters and other high-profile figures, including hip-hop impresario Sean "Diddy" Combs on a bribery and gun possession charge in 2001.
Brafman told ESPN's Sal Paolantonio that Burress is "fully cooperating" with authorities.
When asked by Paolantonio about the whereabouts of the gun involved in the incident, Brafman said "we're dealing with that today with the police."
Burress, who was out Friday night with Giants linebacker Antonio Pierce, was treated overnight and released from a New York hospital on Saturday afternoon.
According to an NFL official, the bullet went through the skin and muscle tissue of Burress' right thigh and did not hit any major arteries, and that there were no broken bones, Paolantonio reported.
NFL handgun policy prohibits players carrying weapons on NFL premises and NFL-related functions. It also prohibits any player having a gun without a proper permit or registration.
The New York Post reported that, according to records, Burress does not have a permit to carry a gun in New York.
Burress had a concealed-weapon permit issued to him in Florida but records show it expired in May and New York does not recognize out-of-state permits anyway, the newspaper reported. A report in the Daily News indicated the same thing.
ESPN legal analyst Roger Cossack reports that Burress could face up to seven years in prison if convicted on the felony charge of carrying a concealed weapon without a permit.
Giants general manager Jerry Reese told reporters Sunday he had yet to speak to Burress.
"I reached out to him," Reese said. "I did not get a return phone call."
Reese told The Associated Press that Pierce had been interviewed by NFL security about the incident at the team's hotel Saturday. The New York Daily News reported that Pierce had tried to hide Burress' gun.
"Antonio is working on trying to beat the Redskins right now," Reese said before kickoff. "That's where his focus is and where it should be right now."
Pierce deflected several questions after the game. He wouldn't say whether he has a lawyer and when asked if he is concerned about his own situation, Pierce replied only: "No. I'm fine where I'm at."
"I am not answering any questions about the incident that happened Friday night," the linebacker said. "If you have anything to say about the Washington Redskins, this game and moving forward, I'll answer it. Anything else, I'm not answering."
Giants coach Tom Coughlin said he spoke to his players about Burress' situation but wouldn't get into specifics.
"We all are upset about what happened with Plaxico, and hopefully he's going to be fine and so on and so forth. That's our first concern," Coughlin said. "Once that was taken care of, we knew that he was OK, then the guys got right back to focusing on the reason we were here."
Coughlin wouldn't address Burress' future with the Giants, saying only, "Questions of that nature will be discussed going forward, I'm sure."
Police and NFL security are investigating whether there was a third Giants player who was present or involved, at the very least for gathering more information on the incident, sources told ESPN's Chris Mortensen.
"I'm disappointed this happened and that any of our guys would put themselves in this kind of situation," Giants president and CEO John Mara said Sunday. "Our first concern is for Plaxico's health and well-being. We were very relieved to find out he is OK. But yeah, I'm disappointed."
Neither Reese nor Mara would say what Burress' status with the team might be going forward.
"I want to wait until we find out all the facts and circumstances before we make any determination," Mara said. "I don't know what happened there, and until we find out exactly what happened, I'm not going to make any comment or make any decision about what his future is."
The team is considering placing Burress on the non-football injury reserved list, which would make him ineligible for the remainder of the season, sources said. It also would allow the Giants to recover some money already paid to Burress.
Additionally, a source told Mortensen that Burress has as much as $4.5 million tied to play-time incentives and active-roster status.
Information from The Associated Press and ESPN senior NFL analyst Chris Mortensen was used in this report.