The Harry Potter author has become an increasingly controversial figure in recent years over her stance on trans rights which Norton has been supportive of.
Speaking to The Times, Norton said not interviewing people because you disagree with them "feels wrong".
The broadcaster and author said: “Am I suddenly the f**king moral arbiter of the world who says who can be on TV or can’t? No."
Norton added that he “wouldn’t have her on to air her views, she has the right to still wang on about her crime novel”.
He concluded by saying: “The easiest thing would be to not have her on, but that didn’t seem right."
Creators of West End hit Six: The Musical Lucy Marlowe and Toby Ross last year pulled out of an interview with Norton when he was still at the BBC after finding out they would be sharing a platform with Rowling.
At the time, they released a statement on social media that said: “We want to apologise to anyone who was looking forward to hearing us being interviewed on the radio today. Sadly, we had to withdraw as we didn’t feel comfortable being on the same billing as JK Rowling. We strongly disagree with her transphobic views and statements, and we don’t want to feature as guests on a show where she is promoting her work until she has made significant efforts to make amends with the trans community.”
JK Rowling refutes that she is transphobic in any way.
The author recently released her latest novel in her Strike detective series – The Ink Black Heart – a 1000 page thriller about a cartoonist criticised for appearing to have bigoted reviews.
Online reactions to the book have been largely negative.
Watch below: Harry Potter says social media is 'gift' for online trolls.