Eckhart and Jenkins for Rum Diary
Withnail And I's Bruce Robinson is to direct the project, which stars Johnny Depp as a struggling journalist named Paul Kemp.
According to the Hollywood Reporter, Eckhart is in discussions to play Sanderson - a wealthy businessman who introduces Kemp to a better lifestyle but clashes with him over the affections of a woman.
It is also thought that Jenkins will play the boss of the rundown newspaper where Depp's character works.
Filming is scheduled to begin in Puerto Rico on March 30th.
Eckhart was recently seen as Harvey Dent/Two-Face in The Dark Knight, a character which he claims may make a return if a sequel goes ahead.
Jenkins - who has been nominated for an Oscar for his role in The Visitor - was last seen in the Coen brothers' screwball comedy Burn After Reading.