Giants co-owner John Mara previously told the media the two sides would begin negotiating "sooner rather than later."
Beckham is set to enter the final year of his rookie contract.
Although there was talk of a potential holdout, OBJ reported to Giants camp on the heels of a 2017 season that saw him miss all but four games because of injury.
In the previous three seasons, the 25-year-old Beckham was named to the Pro Bowl each year. He also finished each of those campaigns with at least 90 receptions for 1,300 yards and 10 touchdowns.
During the 2018 season, Beckham will earn $8.46 million after the Giants picked up the fifth-year option on his contract.
New York struggled mightily last season without the 2014 first-round pick in the lineup, finishing with the NFL's second-worst record at 3-13.
With Beckham in the fold and running back Saquon Barkley on the team after getting taken with the No. 2 overall pick, the Giants have a chance to bounce back this season. Barkley's presence should make Beckham an even more dangerous threat since the Giants haven't had a quality running game throughout his NFL tenure.
Regardless of whether the Giants are able to get a deal done with Beckham before next offseason, they have the ability to keep him in the Big Apple by using the franchise tag.