The agitators have demanded the producers to drop "The Revenant" actor's name from the list and cast a Middle eastern actor to play the poet.
Currently, the name of the 41-year-old "The Wolf of the Wall Street" actor is doing rounds for the lead role while the "Iron man" actor Robert Downey Jr in second lead as Iranian mystic Shams of Tabriz.
The controversy evoked when the film's screenwriter David Franzoni disclosed his casting plans, in an interview with the Guardian.
The petitioners called it the "Hollywood whitewashing" for not giving Muslim actors positive roles and typecasting them as negative only.
"Casting Leonardo DiCaprio as Rumi rewrites history, takes possession of Muslim accomplishments and gives the credit to a white man," said Valerie Janovic, a person who set up the petition.
"Now, when people think of Rumi, they'll picture him with pale skin, blond hair and blue eyes. Muslim actors are readily typecast as terrorists but when a movie portrays a Muslim in a positive light, they are shunted off to the side to make room for another white actor. The casting for the Rumi movie is not yet final and together we can change it," he added.