Dye, 80, has been asymptomatic for coronavirus, according to his son, Pat Dye Jr., an NFL agent.
"As has previously been reported, my dad has tested positive for the COVID-19 virus," Dye Jr. told ESPN in a statement on Thursday. "However, his positive test occurred a number of days ago during a routine precautionary test pursuant to his hospitalization for kidney-related issues.
"He has essentially been asymptomatic for the virus and is resting comfortably. We fully anticipate his release from the hospital in the next few days once his kidney function is stable. On behalf of my family, I want to thank everyone for the overwhelming support for Dad and our family upon the reporting of this news."
Dye guided the Tigers to a 99-39-4 record in 12 seasons from 1981 to 1992, winning at least a share of SEC championships in 1983, '87, '88 and '89. His Auburn teams won at least 10 games in a season four times and bowl games six times.
He was inducted into the College Football Hall of Fame in 2005, the same year the playing field at Auburn's Jordan-Hare Stadium was named in his honor.
Dye was a three-time SEC coach of the year and 1983 national coach of the year. He coached a Heisman Trophy winner (Bo Jackson, 1985); an Outland Trophy and Lombardi Award winner (Tracy Rocker, 1988); and 21 All-Americans, 71 All-SEC players and 48 academic All-SEC players.
Dye was Auburn's athletic director from 1981 to 1991. He also coached at East Carolina from 1974 to 1979 and Wyoming in 1980 and had a 153-62-5 record in 19 seasons overall.
He had been spending much of his time in recent years at his farm in Notasulga, Alabama.