Coach Joe Judge said Thursday that the Giants "dodged a bullet" and would look to get Jackson ramped back up. Jackson wasn't seen outside at Thursday's practice.
Jackson's injury is not considered serious, and he has his sights set on Week 1, the source added.
Jackson rolled his left ankle while defending a pass on Wednesday. After the practice, he hobbled over to the cart and took a ride inside.
Jackson signed a three-year, $39 million deal this past offseason. He spent the first four years of his career with the Tennessee Titans.