Martin Scorsese’s representatives have been holding talks with Apple Inc., Netflix Inc. and others, as they seek a new company to produce or distribute the director’s next big-budget film, according to people familiar with the matter. This shift would be the second time in a row the director’s project has become too costly for its original studio.

The project, “Killers of the Flower Moon,” had been slated for production at ViacomCBS Inc.’s Paramount Pictures, but then the movie’s cost ballooned to more than $200 million,...