Sources told the New York Daily News that the Houston Texans, St. Louis Rams and Philadelphia Eagles also contacted Burress on Tuesday, but if things go well with Coughlin and other team officials Wednesday, the Giants would be the receiver's first choice.
"I really don't know what I'm going to say," Burress told The Star-Ledger. "I'm just going to go in there tomorrow and speak from the heart, be truthful with him and let (Coughlin) know how I feel. Whatever comes out is going to come out. I'm pretty sure there are things he wants to say, too.
"I do love New York. My fan base here has been great to me. But it's not just about football; there are just a lot of things that go into it. But after this, I'll know a lot more."
Burress, 33, used to be one of the Giants' most productive offensive players, and he caught the winning touchdown pass against the New England Patriots in Super Bowl XLII. Then in November 2008, a handgun that Burress brought into a New York nightclub accidentally went off, shooting the receiver in the leg. He served nearly two years in prison on a gun charge -- New York has some of the strictest gun laws in the nation -- and was released in June of this year.
Burress has been the subject of widespread rumors about which team will sign him this season. The Giants weren't believed to be interested, but that has changed in recent days, with owner John Mara saying Monday that the team indeed was open to the possibility.
The NFL's post-lockout rules state that free agents cannot meet with teams at their facilities until Friday. It's unclear whether off-site meetings are permitted. The Star-Ledger reported Tuesday that the Giants are trying to get that part clarified by the league. If they're permitted, a meeting Wednesday is likely; if not, the sides will sit down Friday.