Reese, who attended the NFL's annual scouting combine Saturday, said he's planning for all scenarios, including keeping the suspended wide receiver who shot himself in the leg at a nightclub last season.
"I hope he's motivated, but the legal process is what's most important right now and his health is what's most important right now," Reese said. "But we'll prepare as if he's not going to be here, and if he is, it's a bonus."
Burress faces felony charges of criminal possession of a weapon relating to the shooting, which could result in a prison sentence of 3½ to 15 years if he's convicted.
Reese would not comment on the e-mail sent last week by Drew Rosenhaus, Burress' agent, to NFL teams saying three clients wanted to be traded. Burress was one of them.
Despite the trouble surrounding Burress, Reese said he would take the 31-year-old player back with some caveats.
"We want him to be like everyone else as far as the team structure is involved," Reese said. "Plaxico is a New York Giant right now, so I don't know what it means to 'have him back.' He hasn't gone anywhere yet."
The disparity between Burress' presence and absence was remarkable.
With Burress, the Giants were one of the league's best. He made the winning catch in the Giants' 2008 Super Bowl victory, and helped lead them to an 11-1 record last season.
Without him, it was easier for defensive coordinators to game plan against the Giants.
Eli Manning threw three touchdowns in the five games after Burress was suspended, and the Giants wound up losing their first game in the playoffs.
Reese said he and Burress have traded e-mails, but have not spoken since the season ended -- though team doctors have been in touch with Burress.
"I'm assuming he wants to be back, I don't know why he wouldn't," Reese said. "But a lot of things have to work out before that happens. I don't know what the league will do as far as suspension stuff."
Burress is only one of the Giants offseason concerns.
Running back Derrick Ward, who ran for 1,025 yards last year and was part of the Giants 1,000-yard rushing tandem, could hit the free-agent market next week. The Giants put the franchise tag on their other 1,000-yard runner, Brandon Jacobs, on Feb. 13.
Reese is trying to reach deals with each of his top two runners and work on a contract extension for Manning, last year's Super Bowl MVP.
"We've been having some conversations in respect to Eli," Reese said. "We'll get that done in time."
The more pressing priority is the running game.
Reese would like to complete a long-term deal with Jacobs, to provide salary cap room, and hopes to re-sign Ward before he hits the free agent market on Feb. 27.
"The tag gives us a little more time, but it has make sense for both sides," Reese said. "We've been fortunate because we've had three [running backs]. With Derrick, we have some conversations going on right now."