The Giants open their season on the road on Sept. 10 against the Dallas Cowboys.
It's "not out of the question he could miss a week or two of the regular season," according to one source.
Beckham left Monday night's game against the Cleveland Browns after taking a hard hit to the left leg from Browns cornerback Briean Boddy-Calhoun. An X-ray during the game was negative. He underwent an MRI on Tuesday that confirmed a sprained ankle.
"I'm taking it one day at a time," Beckham said in a text to ESPN's Josina Anderson on Wednesday morning.
Despite jogging into the locker room and expressing optimism after the game, Beckham felt "very sore" on Tuesday, according to another source. He's likely to miss the Giants' final two preseason games.
Coach Ben McAdoo said the team would see how Beckham responds to treatment.