The original movie, which was released in 1965, starred real-life couple Richard Burton and Elizabeth Taylor.
According to Examiner, the couple have been eyeing a film that they could star in together now that the Twilight franchise has come to an end.
The Sandpiper centers on a single mother who has an affair with the married headmaster at her son's school.
successful run at the box office as Bella Swan and Edward Cullen.
Bel Ami actor Pattinson "recognizes there's a certain screen magic when he and Kristen are together," a friend of the stars claimed.
At the moment, Pattinson is said to be contemplating his personal relationship with Stewart and will make a decision in the New Year.
Watch a clip from The Twilight Saga: Breaking Dawn - Part 2 below: