Rix and fellow former Chelsea coach Gwyn Williams have denied "all and any allegations of racial or other abuse" which the BBC has said date back to the 70s, 80s and 90s.
Seven former Chelsea players have now accused Williams or Rix of historical abuse, following previous claims made by three players in January.
Chelsea have said they are taking the allegations "extremely seriously" and added: "The allegations will be fully investigated. We are absolutely determined to do the right thing, to assist the authorities and any investigations they may carry out, and to fully support those affected which would include counselling for any former player that may need it."
The BBC said it had spoken to four players, one of whom alleged that he was subjected to an "exhaustive list" of racial slurs while another described the club as "institutionally racist" at the time the incidents were alleged to have occurred.
Former England and Arsenal midfielder Rix, 60, joined the Stamford Bridge club in 1993 and left in 2000, a year after being jailed for six months for having sex with a 15-year-old girl.
Williams, 68, joined Chelsea in 1979 as youth development officer and worked as assistant manager under former boss Claudio Ranieri before leaving the club in 2006.
Last year Rix, who appeared for England at the 1982 World Cup, was admitted to hospital after suffering a heart attack.
Rix skippered Arsenal from 1983 until 1986, having joined the Gunners as a youth team player in the 1970s. He made 464 appearances for the North London club and won the 1979 FA Cup Final against Manchester United, providing the cross for Alan Sunderland’s last-minute winner.
After retiring, he became a manager and had stints with Chelsea, Portsmouth, Hearts and Oxford United.
Born in Doncaster in 1957, Rix began his career with Arsenal in 1975.