The Gangster Squad actor is not yet officially on board, but film bosses are expected to offer him the part soon, reported The Wrap.
Josh, 45, is said to be "likely to accept" the role in the fourth movie in the Jurassic Park franchise.
He would join Bryce Dallas Howard, Nick Robinson and Ty Simpkins, who are all thought to have signed up.
So far little is known about the 3D dinosaur thriller, as plot details are firmly under wraps.
Jurassic World, directed by Colin Trevorrow, is scheduled to be released in June 2015.
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