Robert Pattinson and Kristen Stewart may remake Richard Burton-Elizabeth Taylor movie 'The Sandpiper'

"Twilight" stars and once-again off-screen couple Kristen Stewart and Robert Pattinson are reportedly considering making another movie together -- and following in the footsteps of another famous Hollywood couple.

Pattinson and Stewart are mulling over the idea of starring in a remake of the 1965 film "The Sandpiper," which starred Elizabeth Taylor and Richard Burton, according to Hollywood Life. The film, directed by Vincente Minnelli, is about a single mother (Taylor) who begins an affair with the married headmaster (Burton) of the school her son attends. Eva Marie Saint played Burton's wife in the movie.

Pattinson "recognizes there's a certain screen magic when he and Kristen are together," a "buddy" of the actor tells the site. The anonymous friend also takes a swipe at Stewart's fling with "Snow White and the Huntsman" director Rupert Sanders: "Besides, there's less chance she'll get in trouble again."

"The Sandpiper" was a box-office hit thanks to the star power and scandal surrounding Burton and Taylor, but critics gave it pretty harsh reviews. The movie is probably best remembered now for its Oscar-winning original song "The Shadow of Your Smile."