Shepard, 23, was added to the team's injury report Saturday because of an illness, but the team wants to test him in pregame warm-ups before making any determination, a source told ESPN's Adam Schefter.
Shepard will miss Sunday's game due to migraines, according to Schefter.
He missed two games earlier this season with an ankle injury but returned in Week 9 and stepped in as the No. 1 receiver for the Giants, who have lost Odell Beckham Jr. and Brandon Marshall for the year.
In two games since his return, Shepard has totaled 16 catches for 212 yards, including 11 catches for 142 yards in last week's 31-21 loss to the San Francisco 49ers.
The Giants have lost three straight and enter Sunday's game with a 1-8 record.