Burress pled his case to his former coach in a face-to-face meeting that lasted nearly 90 minutes at Giants headquarters in East Rutherford, N.J., on the first day of training camp.
Burress wasn't made available to the media, and he left via a side door to avoid contact.
Osi's not a happy camper
Burress arrived at 6:30 p.m., and left shortly after 8, spending nearly an hour with Coughlin. He then spent 15 minutes each with president John Mara and general manager Jerry Reese.
When Burress arrived, and again on his way out of the complex, he had conversations with many of his former teammates and coaches, notably running back Brandon Jacobs, who restructured his deal this week to remain a Giant.
Only time will tell if Burress has a chance to join him.
"What I have to hear is sincerity," Coughlin said late Friday afternoon, roughly two hours before the scheduled meeting, the first between the two since the soon-to-be 34-year-old receiver and Super Bowl XLII hero was imprisoned for almost two years on a weapons possessions charge.
"I am looking forward to it. I will be opened minded about it," Coughlin said. "It's an opportunity in a confidential setting to sit down, and what I feel is it will be Plaxico's opportunity to speak. I am going to listen and decipher. I'll ask questions, but basically I would like to hear what he has to say."
"Ownership would like to think that we can sit down and talk about it and secondly, you know, this is business," Coughlin said. "It's not personal for me. It's business. I can separate the two. I have no ego in terms of what I have to accomplish with regard to him or anybody else. I'm willing to listen."
Coughlin indeed planned to listen, go over what was said, then report back to management to say whether or not the two can work together again.
The Giants insist they are serious about possibly signing Burress, who provided their one true deep threat during his time with the team between 2005 and 2009.
"We don't bring guys in just for the fun of it," Giants general manager Jerry Reese said. "We won't bring a guy in unless we are serious about the possibility of signing him."
Less than a year later, Burress shot himself in the leg in a New York nightclub in late November. He was kicked off the Giants weeks later, and the team fell apart in the playoffs. Burress was jailed the following September after pleading guilty to the weapons charge.
Burress criticized Coughlin after his release, but the coach downplayed it, saying all he wants is commitment from his players.
"When you sign on to go to work for someone, you have to go to work, you have to be there on time," Coughlin said. "What is there to change? When you come down to it, that's the basic ingredient or rule. Jump into the team as hard as you can, as fast as you can, but understand your responsibility, people depend on you."
Burress let down the Giants in 2008. The team was 11-1 and had a chance to make another title run, but the offense disappeared after the receiver was let go.
Veteran David Diehl said Friday that he would be willing to give Burress another chance, simply because of how he can dynamically change an offense.
"If anyone has felt the consequences of his actions, it's him," Diehl said. "For us to sit here and be in the situation where we might get him back, I think we would welcome him with open arms."
However, in May, Diehl talked about Burress potentially not wanting to return to New York so he can simply move on in life.
"If I were in that position, in order to move on and start fresh, you have to get back to square one," Diehl said during an interview with NFL.com. "That's getting back to playing football. That's getting back to yourself, and not only enjoying your family, but enjoying your life and being happy again. For him, I think that's somewhere else."
The Associated Press contributed to this report.