A little over a year ago, one would have been hard pressed to find almost anyone who knew or even recognized Carey Mulligan from her handful of small roles. But thanks to her star-making, Oscar and Golden Globe-nominated turn in An Education, the British actress has shot up the ranks to become a serious A-lister.

Now she’s the latest name attached to play Eliza Doolittle in the planned remake of the classic musical My Fair Lady.

Actress Emma Thompson, who has penned the script for the new film, told the BBC she believes Mulligan is a lock, while the part of her male sparring partner remains uncast. “I think Carey is set to play it, yes,” she said. “But we still don’t know about [Henry] Higgins.”

One name that has been bandied about for the part is Hugh Grant, an idea that sits very well with Thompson. “I love Hugh so I’d love him to do it, he might want to, he might not want to, so we don’t know yet. But hopefully we’ll make it later this year.”

It should be noted that none of this is official just yet and Mulligan is only the latest in a long list of names that have circled the part. Last summer Keira Knightley was said to be a sure thing after beating out blonde bombshell Scarlett Johansson. Knightley reportedly backed out when plans for the long-gestating project continued to stall.

My Fair Lady is the story of  rough-around-the-edges Eliza’s efforts to make herself a lady under the tutelage of Mr. Higgins. The first film of the Broadway musical starred Rex Harrison as Higgins and the inimitable Audrey Hepburn as Eliza.