ESPN's Chris Mortensen reported Monday that Allen is dealing with a right elbow injury to the ulnar collateral ligament and related nerves. His status remains uncertain for Sunday's game against the Minnesota Vikings.
"We'll see," McDermott said when asked if Allen would play in the game.
"We will see how he does," McDermott said. "We use common sense and, obviously, we factor a lot of things in, a medical report being one of them and our doctor's wisdom and knowledge."
McDermott declined to say if Allen has thrown since Sunday and whether he has sought a second medical opinion.
Allen was not present Wednesday during the portion of practice open to the media.
Allen was injured during the last drive of the 20-17 loss to the New York Jets. Jets defensive lineman Bryce Huff got past backup right tackle David Quessenberry, in for injured tackle Spencer Brown, and hit Allen's throwing arm, which resulted in a strip sack recovered by Buffalo.
After the hit, Allen was seen holding his right elbow and trying to shake out his arm.
Two plays after the hit, Allen threw a pass intended for wide receiver Gabe Davis 69.3 yards in the air -- the longest pass attempt over the past six seasons, per NFL NextGen stats. It fell incomplete and ended the game.
Allen dealt with an injury to the UCL in his right elbow during his rookie season and missed four games. He has not missed a game since.
"There's some slight pain," Allen said after the game, "but we'll get through it."
Before the injury, Allen was going through a rough stretch. In the past six quarters since halftime of the win over the Green Bay Packers in Week 8, he has zero touchdown passes and four interceptions and has completed 47.9% of his passes.
It's difficult to overstate the role Allen plays on the offense. He has accounted for 23 of the Bills' 25 offensive touchdowns, either with his legs or his arm. The quarterback has accounted for 82% of the offense's total yardage and 92% of its touchdowns, both highest in the league.
"He's optimistic," tight end Dawson Knox said. "He's a dog, that's a great word for him cause he's gonna be in that training room 24/7 doing everything he can to get back on the field and from what I can tell he's in a pretty good mood."
If Allen is unable to play, backup Case Keenum, whom the Bills acquired in a trade with the Cleveland Browns in the offseason, would step in and face his former team. Keenum has played in two games this season when both were well out of reach. He would face his former team, alongside wide receiver Stefon Diggs, whom he connected with on the Minneapolis Miracle play in the 2017 divisional round of the playoffs.
"He's a winner," Diggs said. "He's a dog, people don't -- I mean Case is a professional and all those good things, but when he gets out there he's still competing at a high level. He gives you that confidence that you can win, whether it's with his arm or whether he's improving or making things happen. So, I have complete confidence in him."
McDermott said the Bills brought in Keenum "for a reason."
The Bills are dealing with other injuries as pass-rusher Greg Rousseau is week-to-week and safety Jordan Poyer, linebacker Tremaine Edmunds (groin/heel) and left guard Rodger Saffold (vet rest/back) also missed Wednesday's practice.