The promising defensive tackle has been out with a back issue for a few weeks now and the hope was that he would be ready for the Sept. 5 opener.
"He was doing well and then he had a little setback," Coughlin said. "This clouded the issue again. It is not clear when he can go."
Coughlin had no timetable for Amukamara's return, but the Giants head coach understands it could be several weeks before last year's first-round pick returns as the starting cornerback.
Amukamara was starting in place of Terrell Thomas, who aggravated his surgically repaired right ACL early in camp and has been out indefinitely. With Amukamara potentially missing a month or more, the Giants will likely go into the season opener against Dallas without two of their top three cornerbacks.
Thomas wrote on his website that his goal is still to play in the season opener.
"It feels strong and no swelling," said Thomas, who was able to avoid a third surgery on his knee. "I am getting back to my old self; my goal is to still play in the season's opener."
Coughlin didn't seem as optimistic about Thomas, who continues to rehab his knee.
"Not according to what I am reading, no," Coughlin said when asked if a Thomas return against the Cowboys was realistic. "But I think you have to always give way to hope."
Coughlin had more positive news about starting left tackle Will Beatty, who has shown improvement with his back and could begin doing some individual work this week.
"He has had four pretty good days in a row and they feel pretty good about his strength and the direction he is heading in," said Coughlin, who also was happy with backup Sean Locklear's performance at left tackle in place of Beatty.
"[Beatty] probably will get some individual time early part of this week just to see where he is and hopefully he will tolerate that and we can increase the workload."
Also, impressive rookie cornerback Jayron Hosley might be able to shed his protective walking boot for his turf toe in the next few days and begin some light work.
Coughlin also said linebacker Mathias Kiwanuka is sore with a strained groin, but it sounded as if Kiwanuka will be ready to play against the Cowboys. Ahmad Bradshaw's bruised right hand is also improving, according to Coughlin.