Murphy starred on SNL from 1980 to 1984, becoming a hit with characters such as Buckwheat, Velvet Jones and his Borscht-belt comic version of Gumby.
The comedian became upset at SNL producer Lorne Michaels because of an early '90s sketch where David Spade slated Murphy's career following a series of box office flops.
Spade joked as a picture of Murphy was shown: "Look children, a falling star... quick, make a wish!"
Murphy admitted that the insult angered him for many years, but said that he is now open to hosting SNL for the first time since 1984.
He told Rolling Stone: "They were sh**ty to me on Saturday Night Live a couple of times after I'd left the show. They said some sh**ty things. There was that David Spade sketch, I made a stink about it, it became part of the folklore.
"What really irritated me about it at the time was that it was a career shot... I felt sh**y about it for years, but now, I don't have none of that [anger]."
Earlier this week, Murphy told Today that Tower Heist co-star Ben Stiller had asked him to cameo on SNL this month, but it didn't fit his schedule.
Murphy also revealed that he is considering returning to stand-up comedy, but only if the right opportunity comes along.
"If I ever get back on stage, I'm going to have a really great show for you all. An hour and a half of stand-up and about 40 minutes of my sh**ty band... But I haven't done it since I was 27, so why f**k with it? But that's just weighing both sides," he said.
"It comes up too much for me to not do it again. It's like, when it hits me, I'll do it, eventually."
Tower Heist opens on November 2 in the UK and on November 4 in the US.
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Watch a clip of Eddie Murphy from Saturday Night Live below: