Beckham had soreness and swelling in his left leg, but did light jogging at practice on Tuesday and Wednesday with new strength and conditioning coach Aaron Wellman. He ran sprints Thursday.
Coach Ben McAdoo said Wednesday that Beckham was close to a return and was "absolutely" making progress.
Beckham was injured when he became entangled with cornerback Janoris Jenkins during Sunday's practice. He limped off the field and the Giants said afterwards he had been cleated and had lacerations on his left leg.