Stewart famously acknowledged in July that she had been involved in a fling with her married Snow White and the Huntsman director Rupert Sanders while dating Pattinson, but the Twilight couple are rumoured to have recently reconciled.
Speaking to Seventeen, Greene insisted that the media should be covering the final Twilight film rather than the cast's personal lives.
"Hopefully, it won't taint it and people will still be able to enjoy the movie," Greene told the publication.
She went on to say: "I think a lot of people see us as our characters; I really want them to still be able to do that."
Stewart and Pattinson have both remained coy on the status of their relationship when questioned in the press over the last week.
The pair were snapped sharing a passionate kiss at Stewart's Hollywood home late last month.
Breaking Dawn - Part 2 will open in cinemas worldwide on November 16. Watch the trailer below: