Van Riemsdyk was unavailable for comment.
Briere did not skate Wednesday because of "little headaches. You're kind of like almost in a fog walking around," he said. "I was always wondering before when I saw guys with concussions: 'How does it really feel when you're in a fog?' Now I know; you're not quite yourself."
The veteran center said he had three or four concussions earlier in his career, but in those instances he did not have symptoms and continued playing.
Briere said he was "confident I'm not very far away. It's not like I'm worried about my career or the season or anything like that. I really think I'm that close."
He still has not been able to take contact in practice, and that is the next step on his road to returning.
In a minor-league deal, the Flyers acquired Hershey Bears right winger Matt Ford, 27, for Adirondack defenseman Kevin Marshall.
The 6-foot-1, 207-pound Ford, who was assigned to the Phantoms, had 10 goals and 18 assists with Hershey. He had 26 goals for AHL Lake Erie last year.
Ford, a California native, was once a teammate of Sidney Crosby's at a Minnesota prep school.
Marshall, 22, played 10 games with the Flyers this season and 32 with the Phantoms (five points).
Because Nashville could lose defenseman Ryan Suter to free agency after the season, there has been speculation he could be dealt before the Feb. 27 trade deadline. The Flyers have shown interest.
"Obviously he's a good player, but I think we need to worry about who's in the locker room right now," Claude Giroux said. "The trades are not up to us. That's not our job, and I think it's important to stay focused on the things we have to do."
Suter said he was "focused on playing in Nashville" and hoped to stay there.
The Predators are the NHL's hottest team.
"If we were struggling," Suter said, "they'd probably be trading me if I hadn't signed."
After being a healthy scratch for the last seven games, veteran defenseman Andreas Lilja returned to the lineup Thursday, replacing rookie Erik Gustafsson.
Coach Peter Laviolette said he wasn't disappointed with Lilja's play when he removed him from the lineup.
"Sometimes decisions aren't necessarily based on somebody not playing well," he said. "It's more about we have young players coming up through the organization and you've got to give them an opportunity as well."
Gustafsson, who returned to the lineup Jan. 14 after missing two-plus months because of wrist surgery, is plus-6 in 12 games.
Laviolette praised Gustafsson's play before adding that Lilja (plus-3) "has worked extremely hard with a real positive attitude."