The Vicar of Dibley star is said to have impressed during her stint as a judge on talent show Superstar, reports The Sun.
"Dawn played a very important part in the show," said an ITV source. "Her wit and warmth were very much valued.
"She is also incredibly down-to-earth and a real joy to work with on set. We would love to work with her again on other shows.
"Despite being new to this, she played an absolute blinder. Watch out, David Walliams!"
French was tipped to join the panel of ITV's Loose Women last year.
Ben Forster was crowned the winner of Superstar earlier this week.