Moyles is contracted to stay with the station until 2014, but controller Ben Cooper is quoted by The Mirror as suggesting that a younger DJ may soon take over the morning slot.
"He has a contract but whether it's for breakfast or not is for me and him to know," Cooper said. "Success will be down to average age. There'll be changes but no night of the long knives."
On his future plans for Radio 1, Cooper teased: "It was great when Jamie Oliver went to Number 10 about school dinners. I'd like us to be the unofficial party of young people."
Moyles signed a £1.25m deal to stay with Radio 1 in July.
However, his breakfast show recorded a weekly audience of just 7.16m in the third quarter of 2011, down on the 7.44m in the previous quarter.