The Giants have been without Jennings since he sprained the MCL in his left knee during a 30-20 victory over the Atlanta Falcons on on Oct. 5.
On Monday, Coughlin had told reporters Jennings "wasn't ready to go," according to the New York Post.
Jennings said he needs to get back to the point where he's cutting and that his movement is linear right now.
"When the time is right I’ll be out there," Jennings said. "Nobody wants me to be out there more than I do. Organization, Giants fans everybody can rest assured I’m doing what I can do."
Jennings is in his first season with New York. The 29-year-old has rushed for 396 yards and two touchdowns on 91 carries in five games this season. He also has 109 receiving yards.
Rookie Andre Williams has received the bulk of the carries with Jennings out. The former Boston College star has rushed for 280 yards and two touchdowns on 89 carries this season.
The Giants (3-4) host the Colts (5-3) on Monday.
- Andrew Melnick