Tarantino has pitched a story idea to Abrams and the duo is planning to develop a movie at Paramount studio, confirmed The Hollywood Reporter.
Tarantino is eyeing to direct the potential project.
The studio did not comment.
Abrams had rebooted the franchise in 2009 with "Star Trek" and also went on to helm "Star Trek Into Darkness", before hitching his wagon to Lucasfilm's "Star Wars: The Force Awakens".
He also serves as a producer on the franchise even as he has signed up to direct "Star Wars: Episode IX", which releases in 2019.
"The only thing that limited them was their '60s budget and eight-day shooting schedule. You could take some of the classic 'Star Trek' episodes and easily expand them to 90 minutes or more and really do some amazing, amazing stuff," he said.