Kovalchuk did not practice with the team Monday, although he did ride the stationary bike and receive treatment.
"Him not being on the ice kind of speaks to his status for tomorrow,"
DeBoer said of Tuesday's game against Carolina.
The 28-year-old winger, who reportedly suffered the injury while back-checking during the team's 4-3 shootout win in Philadelphia Thursday, said he's making progress.
"I'm definitely better than a couple days ago," Kovalchuk said. "We'll see tomorrow."
Following Monday morning's practice, DeBoer said he and general manager Lou Lamoriello would "convene" with the team's medical staff to gain a better understanding of the situation.
Kovalchuk said he understands if the organization wants to proceed with caution.
"You have to be careful," he said. "You've got to get it to 100 percent. You don't want to re-injure yourself and sit for two weeks after that."
Kovalchuk ranks second on the Devils in scoring with two goals and seven assists in 11 games this season and leads the league among forwards in ice time with an average of 25:29 per game. That is almost three minutes more per game than the next on the list -- Anaheim's Corey Perry.
"It's a hole to fill. You don't replace an individual like that,"
DeBoer said. "You have to replace his minutes by committee. We have to do what we did last game, get contributions from different people."
Kovalchuk, who played all but one game last year, doesn't like missing games. So when he does, he considers the injury "serious."
"I missed a game so it is," he said. "I don't miss many games, but I hope it goes away soon."
If Kovalchuk is scratched Tuesday, he could potentially rejoin the lineup Friday when the Devils play the first of a back-to-back, home-and-home set against the Capitals Friday.
With his team riding a two-game winning streak, Kovalchuk joked that they may not be sweating his return.
"The team is doing well," he said. "Doesn't seem like they need me."
Katie Strang covers the NHL for ESPNNewYork.com.