The ABC series will be airing its eighth season when it returns in the fall, but there has been speculation that original cast members Ellen Pompeo and Patrick Dempsey may leave at the end of the next run.
Leigh, who plays Dr Lexie Grey in the series, told TV Line: "The great thing about the show in general is that it has so much leg-room to continue to grow. You can continually bring in new characters, so it's an ER situation in a sense.
"There's always someone coming in, the prospect of interns, the residents now having interns, which we really haven't gotten to see yet... There's a lot of room for new storylines and growth."
Leigh added that she would be happy to take on the mantle of being the titular Grey character on the show, saying: "I can represent the Grey [in Grey's Anatomy] - I'm not going anywhere!"
On the past season of the series, Lexie started a relationship with Jackson (Jesse Williams) despite still having some feelings for Mark (Eric Dane).
Leigh said of the storyline: "It's a complicated situation. As far as Jackson goes, they have so many similarities. They're both very driven, they're both up-and-coming in their careers, they're into the same things… and there's something that's really refreshing about that for her.
"He obviously really cares about her, and she really cares about him... But there is [also] a distraction [element to it], something that sort of eases the pain of the whole Mark triangle situation, which is a really messed-up situation!"
Grey's Anatomy executive producer Shonda Rhimes recently defended last season's finale, saying that she wants to keep the show "fresh".