According to ESPN's Adam Schefter, Shurmur said, "He's on our team right now."
NFL Network's Ian Rapoport reported Monday that OBJ will not take part in team activities until the Giants sign him to a new contract.
Per NFL Network's Kimberly Jones, Shurmur said, "That's my understanding, yeah," when asked if Beckham would take part in offseason conditioning, however.
Beckham is set to enter the final year of his contract in 2018, and he was limited to just four games in 2017 due largely to a fractured ankle.
On Monday, Pat Leonard of the New York Daily News reported the Los Angeles Rams have inquired about a trade. Jones later reported the G-Men are not shopping OBJ and that a trade "probably won't happen."
The 25-year-old Beckham is undoubtedly among the NFL's top receivers when healthy. He made the Pro Bowl in his first three seasons and never finished with fewer than 90 catches, 1,300 yards or 10 touchdowns.
With OBJ out of the fold for most of 2017, the Giants finished 3-13.
On Sunday, Giants co-owner John Mara expressed frustration over questions related to his star wideout, per Paul Schwartz of the New York Post: "I'm tired of answering questions about Odell's behavior and what the latest incident is. I think he knows what we expect of him, and now it's up to him."
Video recently surfaced of Beckham holding what looked to be a brown cigarette while a woman next to him handled a white substance with a credit card.
Beckham's antics both on and off the field have often been called into question throughout his career, but his status as an elite receiver is obvious.
For Shurmur and veteran quarterback Eli Manning, Beckham is likely a major key to their success in 2018.