Speaking on The Late Show with Stephen Colbert the actor, who voices a number of different characters in the television show, said he understood concerns and had been aware of them for years.
The portrayal was criticised most recently in the documentary The Problem with Apu which questioned the stereotypical depiction of Indian immigrants that Apu creates.
“I think the most important thing is to listen to Indian people and their experience with it,” Azaria said. “I really want to see Indian, South Asian writers in the writers room…including how [Apu] is voiced or not voiced.
“I’m perfectly willing to step aside. It just feels like the right thing to do to me.
“It’s come to my attention more and more over the past couple years,” he added.
After the interview aired the creator of the documentary Hari Kondabolu tweeted: “Thank you, @HankAzaria. I appreciate what you said & how you said it.”
Earlier this month The Simpsons’ writers responded to the criticism with an episode where Marge reads her favourite childhood book to her daughter Lisa.
Marge realises the story is more racist and offensive than she remembered and tries to edit it as she reads.
Lisa replies: “Something that started decades ago and was applauded and inoffensive is now politically incorrect.
“What can you do?”
A photo of Apu appears and Marge says: “Some things will be dealt with at a later date.”
Lisa adds: “If at all.”
In January Azaria told reporters at the Television Critics Association’s press tour: “The idea that anybody, young or old, past or present, was bullied or teased or worse based on the character of Apu on The Simpsons, the voice or any other tropes of the character is distressing.”
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On Tuesday night he hinted to Colbert that maybe the time was right for Apu to be voiced by someone else: “I’ve given this a lot of thought, and as I say my eyes have been opened.”
Other characters voiced by Azaria include Moe Szyslak, Chief Wiggum, Comic Book Guy, and Jonathan Frink.