Gray gained 13 yards on three carries in a loss to the Bengals on Sunday.
Gray rushed four times for four yards, caught three of four targets for 50 yards and lost a fumble in Sunday's 29-20 win over the Seahawks.
Gray didn't log any rushes or targets in Sunday's Week 2 loss to Washington, and he returned five kickoffs for 128 yards.
Gray rushed twice for six yards and caught his only target for nine yards in a 28-6 Week 1 loss to Minnesota on Sunday. He added a 22-yard kick return.
Tyrone Tracy is leading the training-camp battle to be the Giants' No. 2 running back behind Devin Singletary, per Ryan Dunleavy of the New York Post, which would push Gray to third on the depth chart.
Gray is in good position to handle a bigger role in his second NFL season, according to Dan Duggan of The Athletic.
Gray played one of the Giants' 56 snaps on offense in Monday's 24-22 win over the Packers.
Gray (calf) is active Sunday against the Patriots, Dan Salomone of the Giants' official site reports.
The Giants activated Gray (calf) from injured reserve Saturday, Dan Salomone of the team's official site reports.
Gray (calf) is listed as questionable ahead of Sunday's game against the Patriots, Art Stapleton of The Bergen Record reports.