Plemons impressed Star Wars producers with a recent taped audition and will now meet director JJ Abrams to discuss the film, multiple sources told The Wrap.
There is no word yet on which part Plemons has auditioned for, but he has apparently emerged as a leading contender to join the sequel.
Plemons's memorable roles include playing mild-mannered thug Todd Alquist in Breaking Bad and nerdy football player Landry Clarke in Friday Night Lights.
Casting for the project has remained largely concealed so far, although Michael B Jordan has revealed that he has had discussions to appear in the movie.
Benedict Cumberbatch and Saoirse Ronan have also been linked to the highly-anticipated movie.
Open auditions were held in London in October for two key roles in Star Wars Episode 7.
Original Star Wars cast members Mark Hamill, Carrie Fisher and Harrison Ford have also been heavily rumoured to be reprising their roles.
Star Wars Episode 7 is scheduled for a December 18, 2015 cinema release.
Star Wars saga behind the scenes - photo gallery:
Catch up on all the latest TV and Movies releases in Digital Spy's Screen Time: