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ITV/Rex Features
According to the Daily Mail, BBC bosses could make the decision in the light of the presenter's falling listener figures in recent official statistics.
A BBC source said: "Vernon is extremely popular and the radio bosses love him. No formal offer has been put in yet - there's still seven months left on Moyles' deal after all - but he is definitely in the frame."
Another added: "Moyles is still the saviour of Radio 1, but he will go sooner rather than later.
"But it works both ways, he only signed a one-year extension deal as he didn't want to be tied down, he wanted the freedom to move on."
Last month, Radio 2's Chris Evans suggested that Moyles would soon leave Radio 1 as he is now older than his listeners.
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