The source said it would take some unexpectedly good news from Wilson's surgeon on Monday to convince the Giants that it's OK for their 2012 first-round pick to return to action.
According to another source close to the situation, Wilson has been very upbeat and has told people he'll be fine again after a couple of days off. His teammates backed that up in conversations Thursday.
"It was good to see him back in the meeting room, bright-eyed and ready to go," fellow running back Rashad Jennings said.
Wilson is upbeat and optimistic by nature, and there's a chance his assessment of the situation won't ultimately jive with the team's.
Wilson had spinal fusion surgery in January to repair a disk problem and wasn't cleared for contact until July 21. He practiced with the Giants for the first week of training camp, but he left the field Tuesday after a collision in practice with guard Eric Herman, and he was diagnosed with a burner.
"As soon as I saw him walk off the field, I started to hurt," Jennings said. "Someone who's been working as hard as he has to get back on the field, when he has a little setback, it's frustrating as a friend, a brother and a teammate."
The Giants sent Wilson to the Hospital for Special Surgery in New York for tests Tuesday night. On Wednesday, they announced that he would sit out the remainder of this week's practices and Sunday night's preseason game.
He's scheduled to be examined Monday by Dr. Frank Cammisa, who is that hospital's chief of spine services and who performed the fusion surgery on Wilson in January.
"Until we hear what the doctors say, I'm just praying that the kid's okay," coach Tom Coughlin said. "When he was cleared to play and he was out here running around with no limitations, I was really excited about that. We're obviously concerned. We just have to wait to see what the doctors say."
If Cammisa doesn't like what he sees, it's possible the Giants could start having discussions with Wilson about an injury settlement and moving on without him.
The Giants are inclined to be very conservative because this is a neck issue, and any aggravation to it could have devastating consequences for Wilson's life after football. It's unlikely they'll want to put him back on the field if they fear any chance at all that he could suffer a significant, debilitating injury to his neck or spine.
The Giants have said they'd be thrilled at Wilson's return, but they also said all offseason that they'd be prepared in case he couldn't play again.
The Giants signed Jennings and Peyton Hillis in free agency and drafted Boston College star Andre Williams in the fourth round. Michael Cox, the seventh-round pick in the 2013 draft, also returns.
Wilson Leaves Practice With Neck Injury
Dan Graziano discusses David Wilson leaving Giants practice on Tuesday with a neck injury.