The former France international has previously criticised United's involvement in the breakaway European Super League, saying the club's owners, the Glazer family, should have taken the views of supporters into account.
"The fans need to be respected," Cantona told the BBC. "Maybe now they need to have voting rights ... Football needs to be democratic."
Cantona said the Glazers should consider letting United's supporters hold a stake in the club, to give them a greater say in major decisions.
