Two weeks ago, the show addressed the topic in its own way, with characters Marge and Lisa Simpson discussing changing times and perceptions. That episode faced severe backlash for not taking the issue and the character more seriously.
Now, Azaria himself says he's given this a lot of thought and "my eyes have been opened."
"I think the most important thing is we have to listen to South Asian people, Indian people in this country when they talk about what they feel and how they think about this character," he said Tuesday night on "The Late Show with Stephen Colbert."
He continued, "And as you know, in television terms, listening to voices means inclusion in the writers' room. I really want to see Indian, South Asian writers in the room, not in a token way, but genuinely informing whatever new direction this character may take, including how it is voiced or not voiced. You know, I'm perfectly willing and happy to step aside or help transition it into something new."
Azaria, 54, added that he hopes the showrunners agree and make some kind of change.
"It just feels like the right thing to do to me," he said.
Many on social media last night praised Azaria's thoughtful response.
The actor's take on the issue comes after the show indirectly addressed the controversy. The writers had Lisa tell the audience, "Something that started decades ago and was applauded and inoffensive is now politically incorrect. What can you do?" The camera then zooms in on a picture of Apu by Lisa's nightstand that reads, "Don't have a cow - Apu."
Fans and critics quickly took to social media to voice their concern about how this was handled.
Comedian W. Kamau Bell said on Twitter, "I think the fact that they put this 'argument' in the mouth of Lisa's character, the character who usually champions the underdogs and is supposed to be the most thoughtful and liberal, is what makes this the most ridiculous (as in worthy of ridicule) and toothless response."
Hari Kondabolu, a comedian who made the documentary, "The Problem with Apu," about this very issue with the character, also took to social media to comment.
"Wow. 'Politically Incorrect?' That’s the takeaway from my movie & the discussion it sparked? Man, I really loved this show. This is sad," he wrote.
In response to the backlash, 20th Century Fox, the network that airs "The Simpsons," told ABC News, "The episode speaks for itself."