The club has pledged to look into the claims, which date back to the duo's time in charge of its youth team, and "fully support" any former players affected.
A total of nine players have come forward with allegations of racial abuse against Rix and Williams, including two white men who have reported instances of discrimination towards their black teammates.
Rix and Williams, who have denied all of the accusations, were investigated when three former Chelsea youth players launched legal cases against them in January, but no police action was taken.
However, both the club and the Football Associations are conducting their own investigations.
"We take allegations of this nature extremely seriously and they will be fully investigated," read an official statement from Chelsea.
"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."
Williams joined Chelsea as a scout in 1976 and later worked with the youth team alongside Rix, who began his Stamford Bridge career in 1993 and went on to serve briefly as assistant manager.