The director is collaborating with Thor screenwriter Mark Protosevich, according to The Hollywood Reporter.
Plans for a follow-up to the third film from 2001 had been put on hold indefinitely after the death of Jurassic Park book author Michael Crichton.
Jurassic Park actor Sam Neill, palaeontologist Dr Alan Grant in the series, said recently that he thought a follow-up is "unlikely" given that the creature designer Stan Winston had also passed away.
A fourth film has been under discussion since 2009, with Jurassic Park III filmmaker Joe Johnston claiming that a script for the project could set up another trilogy.
Watch a trailer for the original Jurassic Park (1993) below: