Eifert, who has a cousin currently deployed overseas, posted a picture on his Instagram account of a jet with a Bengals flag visible through the glass.
Eifert’s post comes one day after San Francisco 49ers quarterback Colin Kaepernick's decision to remain seated during the national anthem before Friday's game against the Green Bay Packers.
Kaepernick said it was a form of protest against the oppression of minorities in the United States.
"I am not going to stand up to show pride in a flag for a country that oppresses black people and people of color," Kaepernick told NFL Media after the game. "To me, this is bigger than football, and it would be selfish on my part to look the other way. There are bodies in the street and people getting paid leave and getting away with murder."
Eifert has expressed appreciation and support for the military many times. He and Pittsburgh Steelers running back DeAngelo Williams engaged in a friendly competition during the Pro Bowl to see how many signatures they could get from military members in Hawaii that week.
On Easter weekend, Eifert wrote about his cousin and military service on his Instagram:
"In November, I’ll have the honor to recognize our service members by wearing camo on the field. It’s a small gesture, its not nearly enough. I salute your service today and everyday - without your sacrifice there is no freedom, no peace, no hope for a safer world. Thank you. #salutetoservice #military #thankyou @usaa @nfl."