A report in the Guardian newspaper alleged that Rix and Williams racially abused and physically attacked black players during the 1990s.
"We take allegations of this nature extremely seriously," a Chelsea statement said.
"We are absolutely determined to do the right thing, to fully support those affected, assist the authorities and support their investigations."
The statement was read out by Chelsea's director of communications, Steve Atkins, in manager Antonio Conte's news conference ahead of Saturday's Premier League match at home against Leicester City.
Eddie Johns, the solicitor representing Rix and Williams, released a statement on his clients' behalf saying: "Our clients deny all and any allegations of racial or other abuse.
"These allegations were the subject of a thorough investigation by specialist officers of the Metropolitan Police Service. The MPS did not consider there was sufficient evidence even to report it to the Crown Prosecution Service. Our clients cooperated with that investigation.
"The allegations in The Guardian newspaper are contained, as we understand it, within correspondence sent to Chelsea Football Club. That correspondence has not been seen by our clients or by us.
"No correspondence has been sent to our clients or us by these individuals or those representing them. We will of course deal with any allegations if made directly to our clients.
"Our clients are cooperating fully with the FA in this matter."
When contacted by Reuters, an FA spokesperson said: "The FA is not in a position to comment on this matter."
(Reporting by Hardik Vyas in Bengaluru; Editing by Christian Radnedge)