Allen was one of 11 players placed on the reserve/COVID-19 list by NFL teams on Monday. All of the moves were the result of positive tests, ESPN's Adam Schefter reports.
Coach Brandon Staley said that Allen's status "is day-to-day right now, and hopefully we'll have some good news on him in the next few days."
Allen, who has been selected to the Pro Bowl each of the past four seasons, leads the Chargers with 86 receptions and 929 receiving yards this season and has four touchdown receptions.
If Allen is vaccinated, he will need two negative tests 24 hours apart and to be asymptomatic for 48 hours before he can return. If he is unvaccinated, Allen will have to stay away from the team for a minimum of 10 days.
The Chargers improved to 7-5 with their 41-22 victory over the Cincinnati Bengals, a game in which Allen had two touchdown receptions and threw a pass to quarterback Justin Herbert for a 2-point conversion.
Los Angeles is currently in second place in the AFC West standings and in possession of the AFC's second wild-card spot.
The Chargers have had a recent run of COVID-19 cases. Defensive tackle Linval Joseph remains in league protocols, while defensive linemen Jerry Tillery and Christian Covington and linebacker Drue Tranquill missed at least 10 days last month. Linebacker Joey Bosa sat out five days and had to test negative prior to the Nov. 21 game against the Pittsburgh Steelers because he was an unvaccinated close contact.
The Associated Press contributed to this report.