The show's revamp, which sees 66-year-old Phillips dropped in favour of popstar Alesha Dixon, 30, has sparked allegations of ageism since it was announced by BBC One controller Jay Hunt earlier this month.
It is believed that 1,369 viewers have contacted the corporation to express their anger at the treatment of Phillips, who has been a panellist since the reality show launched in 2004.
According to The Sun, BBC chiefs are now "panicking" over the growing criticism. However, it is understood that bosses are unlikely to appease fans as Dixon has already signed her contract and they are sceptical over a five-judge format.
Speaking in response to the row, a BBC spokeswoman insisted: "Age or gender has absolutely nothing to do with the decision to replace Arlene on the judging panel. The BBC has numerous mature presenters, including females, in primetime shows.
"Strictly appeals to a wide audience and the BBC has been striving to ensure it stays fresh and relevant for existing viewers and newcomers. Every year the producers consider everything from the celebrities, guest performances, to the dancers and the overall look and feel.
"So the decision to replace Arlene and not one of the other judges was taken as a result of the review process, with the balance and flavour of the panel in mind and nothing else."
Strictly Come Dancing will return to BBC One in the autumn.