Kimberly Jones of the NFL Network reported the update from Shurmur, who noted the contract-year playmaker isn't fully recovered from a fractured left ankle, but he doesn't expect him to get moved despite trade rumors throughout the offseason.
Speculation about Beckham's future heated up in late March when Giants co-owner John Mara didn't fully commit to keeping him.
"We are certainly not shopping him," Mara told reporters. "But, again, when you are coming off a season where you are 3-13 and played as poorly as we played, I wouldn't say that anybody is untouchable."
Meanwhile, the NFL Network's Ian Rapoport reported Beckham "will not set foot on a field without a new contract extension" in place.
Beckham is set to make $8.5 million in 2018 after the Giants exercised the fifth-year option in his rookie deal last April, per Spotrac. If no extension is signed, he'd be eligible to become an unrestricted free agent next offseason, though New York would likely use the franchise tag to keep him.
The 25-year-old LSU product was limited to four appearances last season because of the ankle injury. He previously recorded at least 90 catches, 1,300 yards and 10 touchdowns in each of his first three years.
He posted an Instagram video Monday showing himself pulling an SUV as his recovery continues:
With the trade talk seemingly fading, the question now is whether he'll show up to training camp if a new deal isn't reached.