Tarantino and J J Abrams will produce and Tarantino may direct the Paramount Pictures project, reported Variety.
News of the duo working on the R-rated project first emerged earlier this month. Details of the plot have remained under wraps.
Paramount has released 13 "Star Trek" movies since 1979's "Star Trek: The Motion Picture." The studio rebooted the franchise in 2009 with Abrams directing "Star Trek" and "Star Trek: Into Darkness" in 2013 before moving to 2015's "Star Wars: The Force Awakens." Justin Lin directed "Star Trek Beyond" in 2016.