James Mangold is in talks to take over as director of Indiana Jones 5, the outlets reported.
Vanity Fair spoke to a source who confirmed it was Spielberg's decision to step down.
"The decision to hand over directing duties was entirely Steven's," the source said. "He felt now was the perfect time to let a new director and a new generation give their perspective to the overall story and this film."
Spielberg and producer George Lucas introduced Indiana Jones in the 1981 film Raiders of the Lost Ark. Jones is an archeology professor who went on adventures looking for mystical artifacts such as The Ark of the Covenant, the Sankara Stones, The Holy Grail and the Crystal Skull.
Spielberg directed the four previous films including Indiana Jones and the Temple of Doom, Indiana Jones and the Last Crusade and Indiana Jones and the Kingdom of the Crystal Skull. Lucas produced the previous four too.
Lucas sold his company Lucasfilm to Disney in 2012 for more than $4 billion. Disney began releasing Star Wars films in 2015 but has struggled to develop a new Indiana Jones.
Ford remains attached to reprise his role. Spielberg will produce and Variety sources expect him to remain hands on. Disney has set a July 9, 2021, release date for the film.