Trevorrow recently met with Lucas to discuss the potential project because his time travel comedy Safety Not Guaranteed was well-liked at Lucasfilm, reports Celebuzz.
The meeting between Lucas and Trevorrow apparently took place several months before Lucasfilm was sold to Disney in a multibillion dollar deal.
A source close to the production has indicated that Trevorrow's chat with Lucas went well enough that he is now being seriously considered to direct the next Star Wars movie.
Lucasfilm and a spokesperson for Trevorrow have offered no comment on this latest report.
Many of Hollywood's most prominent directors have been rumoured to be in contention to continue the Star Wars franchise.
Matthew Vaughn, Christopher Nolan and Joss Whedon have all been tipped as potential directing candidates in the press in recent weeks.
Star Wars Episode VII is expected to be released in 2015.
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