The medical drama is currently on its 18th season, having first aired back in 2005.
But now Pompeo believes the show is ready to reach a natural conclusion.
“I’ve been trying to focus on convincing everybody that it should end,” she told Insider. “I feel like I’m the super naive one who keeps saying, ‘But what’s the story going to be, what story are we going to tell?’”
“And everyone’s like, ‘Who cares, Ellen? It makes a gazillion dollars.’”
There are rumours that the next season could be the last, with some actors contracted through to a potential season 19 – but there is no confirmation on when the show might come to its end.