Lawyer Benjamin Brafman wrote in an e-mail to The Associated Press that Burress will turn himself in Monday morning in New York City and "will enter a plea of not guilty later that same day."
"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.
Burress shot himself at a Manhattan nightclub Friday night and was released from a hospital early Saturday, the Giants said.
"As far as we know, he's going to be OK," general manager Jerry Reese said before the Super Bowl champions' game Sunday at the Washington Redskins.
Before the shooting, Burress already had been ruled out of the game because of an unrelated leg injury.
New York police and NFL security are investigating what happened Friday. Giants linebacker Antonio Pierce was interviewed by NFL security at the team's hotel Saturday, Reese said.
Pierce - who started against Washington - reportedly was present for the latest dramatic turn in a tumultuous season of fines and suspension for Burress.
"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."
Neither Reese nor Giants president and CEO John 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."
Reese and Mara said they hadn't spoken to Burress, who hurt his hamstring two weeks ago and was going to miss the game against the Redskins because of that injury.
"I reached out to him," Reese said. "I did not get a return phone call."
Mara repeatedly said the Giants would cooperate with the police and the NFL in their investigations.
Asked if he knows what the scope of those inquiries are, Mara said: "I do not know, no. I guess the circumstances of how he got shot, whose gun it was. There are a lot of questions like that that are still unanswered."
Burress caught the go-ahead touchdown pass in the Giants' Super Bowl victory against the New England Patriots in February, following a regular season in which he scored a career-high 12 TDs. He was rewarded with a $35 million, five-year contract, only hours before the current season.
But his consecutive-games streak with at least one catch ended at 115 last week against Arizona, after he aggravated his hamstring injury during the first series and did not return.
Burress has 35 catches for 454 yards and four touchdowns while constantly drawing double coverage this season.
Off the field, he was suspended for a game against Seattle in October and fined $117,500 for missing a team meeting and failing to notify the Giants of his absence. He said he had a family emergency.
Burress also was fined $45,000 by the NFL for his conduct during a game against San Francisco in which he abused an official and tossed a ball into the stands.
By AP Sports Writer Howard Fendrich