The wide receiver injured his heel during the NFC East side's pre-season loss to the Indianapolis Colts earlier this month.
The 26-year-old told the team's website: "I think that's definitely a target date for me. I think I want to come out and get some regular practice in as well, once the doctors let me and the training staff lets me do so. Just taking it one day at a time.
"In my mind, that's a date that I'm targeting. I'm going to work diligently this week while the team's away and focus on getting myself ready and ready to practice potentially by next week.
"It's been better, feels a lot better, a lot of the swelling has gone down. Obviously I'm out of the boot now, looking forward to better days coming. Now that that boot's off and it's feeling good, I still have some time to recuperate. It feels even better."
The Giants play their final pre-season game against the New England Patriots tomorrow, before facing the Cowboys on September 8.