Per SNY.tv's Ralph Vacchiano, Giants head coach Pat Shurmur said Thursday Beckham is being evaluated for a "special surgery" at a hospital that has left his status for Week 15 uncertain.
Beckham was a limited participant in practice last week before being ruled out for Sunday's 40-16 win over Washington.
Per ESPN's Jordan Raanan, Beckham originally injured his quad during one of New York's games against the Philadelphia Eagles. The three-time Pro Bowler had a season-low three receptions and 35 yards in Week 13 against the Chicago Bears.
Beckham was listed as limited during Wednesday's practice on the Giants' official injury report. He's been susceptible to injuries throughout his career, only playing all 16 games in a season once in five years.
In 12 games this season, Beckham leads the Giants with 124 targets, 77 receptions, 1,052 yards and six touchdowns.
The Giants will look for their fifth win in the past six games when they host the Tennessee Titans on Sunday.