Roger Dunaway, assistant athletic director for Tulane University in New Orleans, said Sunday that Walker's parents had arrived at St. Francis Hospital in Tulsa on Saturday night.
"We're just hoping and praying for the best for Devon and his family," Dunaway said.
Tulane said in a news release Saturday that Walker would need surgery in the next day or two.
The injury occurred on the final play of the first half, hours after Tulane opened the Conference USA portion of its schedule against Tulsa. Tulsa was leading 35-3 and facing a fourth-and-2 with the ball at the 33-yard line on Saturday when the Golden Hurricane called timeout. Tulane then called timeout.
When play resumed, Tulsa quarterback Cody Green tossed a short pass to Willie Carter, who caught it at about the 28, and turned upfield. He was tackled around the 17-yard line, with defensive tackle Julius Warmsley and Walker sandwiching him and apparently smashing their helmets into each other.
Medical personnel from both teams tended to Walker as he lay on the field. FOX Sports reported a hush went over the crowd at H.A. Chapman Stadium as Walker was attended to, and that several coaches were in tears as he was taken away in an ambulance. Spectators bowed their heads as someone on the field led the stadium in prayer.
Dr. Buddy Savoie said during a postgame news conference that Walker never completely lost consciousness and was breathing on his own.
"He was stable when we transported him," Savoie said. "I do not think, based on the information we have, his life was ever in danger."
Tulane's team doctor, Greg Stewart, told The New Orleans Times-Picayune in a report published online Sunday that the player had some feeling in his arms and legs. He also told the newspaper that doctors would need more time to determine the extent of his injury.
Later Saturday, Tulane Athletics said in an email that specialists have been treating Walker for the swelling to the neck, adding he remained stable. It praised doctors attending to Walker at St. Francis Hospital in Tulsa for a "great job" with his care.
Walker is a senior majoring in cell and molecular biology. His brother, Raynard, told The Associated Press that their mother was watching the game on television when her son was injured.
Tulane head coach Curtis Johnson said after the 45-10 loss that while Walker was on the field, Johnson told Walker that he was praying for him and that help was on the way.
He said the mood among players was sombre and called the day his most difficult ever.
"It was tremendous that they finished the game, as I thought about just saying 'Hey look, let's not do anything else. Let's just get on the road and go.' "
Associated Press writer Emily Wagster Pettus contributed to this report from Jackson, Miss.