The "Whiplash" actor and the "Sign of the Times" singer are among five young stars who have been asked to screen test for the movie, according to The Hollywood Reporter.
Tom Hanks is already signed up to play Elvis' controlling manager Colonel Tom Parker in the movie, which will focus on the "Blue Suede Shoes" hitmaker's rise to become music's biggest star, as well as his relationship with Parker.
Born in the Netherlands as Andreas Cornelis van Kuijk, Parker notoriously controlled every aspect of Elvis' career and never allowed him to tour outside the U.S., as he would not have been able to follow his client due to his lack of a passport.
He discovered the singer as an unknown and helped him ink his first record deal and pursue a successful acting career. However, their relationship later became strained as Elvis battled drug and weight problems before his death at just 42 in 1977.
According to The Hollywood Reporter, an announcement on who will play Elvis is expected later this month.