In the rapper's new track "Fall", he calls Tyler, the Creator a "f**got b**ch", which incensed gay rights activists.
Eminem later rescinded the slur, insisting he took things "too far".
"In my quest to hurt him, I realise that I was hurting a lot of other people by saying it," he told radio host Sway last month. "At the time I was so mad... it was one of the things that I kept going back to and going, 'I don't feel right with this'."
In an upcoming interview on his "Rocket Hour" show on Apple Music's Beats 1, Elton tells the rapper he was "happy" when he heard the apology, stating, "You're still as feisty as you ever were which I love. I do like a little bit of feistiness. I'm very happy that you said you don't get to use the word f**got anymore... You're bigger than that."
"I'm glad you said that and cleared that up and that's great kudos to you for that. Well done."
The full interview airs on Saturday, October 13.