Snee's still recovering from his elbow injury, and is working with two surgically repaired hips.
The right guard is still "on track" to start the season, though, according to sources.
Snee has considered retirement, the report said.
Snee did not participate in team drills at OTAs or at minicamp. The company line is that he will give it a shot at training camp and he and the team will take it from there.
Entering his eleventh season out of Boston College, Snee, 32, has been everything the Giants had hoped when selected him with the 34th pick in the 2004 NFL Draft. Snee turned out to be more than just head coach Tom Coughlin's son-in-law, he became one of the best offensive lineman the Giants have ever had.
Snee has been been named to four Pro Bowls and made the NFL All-Pro team three times. He is the last vestige of the Giants' record-setting offensive line that helped the club win two Super Bowls.
If Snee has to hang them up, the Giants have a list of candidates lined up to succeed him. Brandon Mosley has been the "next man up" and has received praise from the coaching staff. He's the clear morning-line favorite.
John Jerry, a UFA who was a starter with Miami is also in the mix and don't forget second-year bull Eric Herman and second-round draft choice Weston Richburg, who is a center by trade but has been lining up at guard as well this spring.