Moyles lampooned Wooton's Twitter gossip about his future at the station on his show this morning (February 29), arguing that tabloid journalists have been predicting his demise for over four years.
Wooton suggested that Moyles's future at the station may not be certain following the switch of Greg James and Scott Mills in the drivetime and afternoon slots.
Launching into a rant about Wooton's comments, Moyles told listeners: "Dan Wooton, who is the showbiz dude, for where I don't know. Seemingly the showbiz dude for Twitter.
"He lost his job at the News of the World and nobody has told him... It's like, 'I am showbiz news man. I do showbiz news'. It's like, 'Dan what are you doing? You're in Greggs queuing'."
He continued: "It's amazing that Dan Wooton knows more than I do. I spoke to Ben the controller of Radio 1 yesterday about these changes. It's all about Scott, Gregg, Danny [Howard]... all these people. Dan Wooton thinks it's all about me.
"By the way, it's nothing to do with me. Now even a story that is nothing to do with me can be turned around to be about me leaving.
"There have been stories about me leaving Radio 1 for the last four years and they're still going."
Concluding his tirade, Moyles said: "I'm not going anywhere.
"Dan, you're a nice guy, shut up. Write about what you know and shut up. He's writing it as fact. Write I'm leaving if you want and the month after that when I'm still here and then again the month after that when I'm still here."
Joking about his previous spat with Sun showbiz journalist Gordon Smart, who has repeatedly predicted Moyles's departure from Radio 1, he added: "[Gordon] said on the front page of The Sun, 'Chris Moyles to get the axe', 'he's gone', 'he's going'. That was four years ago.
"He's the only person allowed to say, 'I predicted this here in The Sun, I was right'."
Moyles has continued his spat with Wooton on Twitter today, writing: "Disappointed that you'd lower yourself to the 'Moyles is leaving (erm, in the future, one day)' story. You're better than that."
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