Singletary is slated to sign a three-year deal with the Giants, Adam Schefter of ESPN reports.
Singletary rushed the ball 16 times for 80 yards in Sunday's 26-3 win over the Titans. He added three catches on three targets for six yards.
Singletary carried the ball nine times for 44 yards and caught all three of his targets for 19 yards in Sunday's 36-22 loss to the Browns.
Singletary rushed the ball 26 times for 121 yards in Sunday's 19-16 win over the Titans. He added four receptions on five targets for 49 yards.
Singletary rushed 13 times for 65 yards and a touchdown while failing to catch any of his three targets in Sunday's 30-6 loss to the Jets.
Singletary rushed six times for 18 yards while catching six of seven targets for 54 yards in Sunday's 24-21 loss to the Jaguars.
Texans offensive coordinator Bobby Slowik suggested earlier in the week that Singletary will likely "share the load" Sunday against the Jaguars with Dameon Pierce (ankle), who is active after missing Houston's last three games, Jonathan M. Alexander of the Houston Chronicle reports.
Singletary rushed 22 times for 112 yards and a touchdown and brought in both targets for six yards in the Texans' 21-16 win over the Cardinals on Sunday.
Singletary again will operate as the Texans' top running back Sunday against the Cardinals with Dameon Pierce (ankle) ruled out for that contest.
Singletary carried 30 times for a career-high 150 yards and a touchdown and brought in his only target for 11 yards in the Texans' 30-27 win over the Bengals on Sunday.