It was previously claimed that the DJ would leave the BBC at the end of his current one-year contract. Reports suggested that afternoon presenter Greg James was being lined up to take over the slot.
However, The Sun claims that Moyles is now working on securing a new three-year deal.
"I'm staying," Moyles is quoted as telling the paper. "We've just got to finalise it. I hate saying that because I like them to think I might leave and then see if I can get nicer perks - like they might pay for tea or coffee in the morning."
The paper adds that the corporation is 'willing' to fork out £500,000 a year over two years to keep Moyles.
A source said: "Talks are going well. He wants to stay and the Beeb wants him. The question is for how long."
Last month, Moyles and co-host 'Comedy' Dave Vitty broke the broadcasting record for the longest-ever show and raised over £2 million for Comic Relief.
> Frank Skinner, Chris Moyles lead Sony noms