Beckum, who missed Sunday's 28-14 loss in Washington due to the ailment, will undergo tests on his hamstring this week. He doesn't believe his hamstring is strained.
"They're just sore, but like I said, it's been lingering all of camp," Beckum said Monday.
Beckum initially began to feel the soreness in practice on Friday. He said he may be dealing with the lingering effects of when he pulled his hamstring during his senior year at Wisconsin. The 24-year-old, now in his third NFL season, also dealt with hamstring problems in training camp last year.
"I'm gonna see how it feels," said Beckum, who added that his muscles might be compensating for another injury, although he is unsure what that injury may be. "Like I said, it's hard not to play, but I gotta look out for the best interests of my hamstrings. I don't wanna try to push it."
Head coach Tom Coughlin seemed frustrated by Beckum's uncertainty about the injury after Monday's practice.
"I would hope so, but again I don't have an answer for that," Coughlin replied when asked if Beckum would be able to return to practice on Wednesday. "Then again, I didn't have the answer on Friday afternoon either."
"I know the coaches wanna get me back," Beckum said, "but when you sit down and think about the best way to heal a hamstring, it's rest. It's one of those injuries that you don't wanna keep trying to hurry back from."
Beckum said his injury isn't painful, but it's "just one of those things where it could be mild and you don't wanna turn it into a tear."
Although Jake Ballard had two catches and 59 yards, the Giants' third-down production suffered without Beckum in the lineup on Sunday. They went 1-for-10 on third downs.
"He's our third-down tight end," Coughlin said. "He's the guy that took the snaps the whole week."
Speaking of Ballard, he has a hip contusion and doesn't know when he'll return to practice.
"I don't know. We'll see," said Ballard. "I did treatment today, I'll do some more treatment tomorrow and hopefully I'll be ready to go (on Wednesday)."
Ballard, who missed some time in the first half against the Redskins after suffering the injury, said his hip feels about the same as it did on Sunday.
The Giants are already depleted from a myriad of injuries, so they really cannot afford to see Beckum or Ballard miss significant periods of time.
Mike Mazzeo is a regular contributor to ESPNNewYork.com.