The singer died at the age of 52 after a concert in Detroit on Wednesday evening, his representatives announced.
In a statement, Cornell’s representative Brian Bumbery said his death was “sudden and unexpected”.
It also said the family would be working closely with the medical examiner to determine the cause and asked for privacy.
ornell died shortly after playing a concert with Soundgarden in Detroit on Wednesday evening.
A spokesperson for Detroit Police confirmed that they received a call just after midnight.
“He was found on the bathroom floor, our medical unit were called and he was pronounced dead on scene,” a spokesperson said.
“A family friend went to go check on him and observed him on the bathroom floor. The body was transferred to the medical examiner’s office and the cause of death will be determined.
“It is being investigated as a possible suicide.”
The show was part of a wider tour and the group had a number of live dates scheduled for later this month.
Sir Elton John led the tributes, tweeting: “Shocked and saddened by the sudden death of @chriscornell. A great singer, songwriter and the loveliest man.”
Led Zeppelin guitarist Jimmy Page added: “RIP Chris Cornell. Incredibly talented, incredibly young, incredibly missed.”
Cornell was born on 20 July, 1964.
As a solo artist, he released four studio albums – most recently 2015’s Higher Truth.
His biggest single in the UK was 2006’s You Know My Name, which was the theme song to Casino Royale, which starred Daniel Craig.