Anne, 76, hosted The Weakest Link from 2000 to 2012.
Following her appointment on quiz show Countdown, other inappropriate comments have resurfaced.
Earlier this week, Channel 4 confirmed that she would replace Nick, who stepped down in December following a decade at the helm.
Anne will be the sixth host and the first female to front the long-running show since it began in 1982.
Express.co.uk has contacted a representative for Anne Robinson for comment.