NFL Network's Ian Rapoport reported Monday it is his "understanding" that OBJ "will not set foot on a field" until an extension is in place.
Later Monday, Giants co-owner Steve Tisch told Ralph Vacchiano of SNY that talks of Beckham holding out are "hypothetical" and that the two sides have begun discussing a contract.
Beckham is set to enter the final year of his deal, and he will make around $8.5 million in 2018 as part of his fifth-year option.
Last summer, in an interview with UNINTERRUPTED, Beckham said he wanted to be the highest-paid player in the NFL.
That was before a fractured ankle limited him to just four games in 2017.
Prior to that, Beckham put up elite numbers his first three years. He registered at least 90 receptions, 1,300 yards and 10 touchdowns, along with being named to the Pro Bowl each time.
Beckham has not come without distractions, though, as he received various fines for on-field antics and caught flak for being part of a Giants' wide receiver boat trip in Miami prior to a January 2017 playoff loss to the Green Bay Packers.
Also, video recently circulated showing Beckham with a brown cigarette while a woman lying next to him handled a white substance with a credit card.
On Sunday, Giants owner John Mara said that no player is "untouchable" when asked about the possibility of trading Beckham rather than giving him a new contract, per ESPN.com's Kevin Seifert.
At just 25, Beckham is an elite wideout when healthy, but he is coming off a significant injury and has missed time in three of his four seasons.
With Beckham missing the bulk of the season, the Giants went just 3-13 in 2017.