The DJ is said to have been offered two different timeslots on the national radio station, but has turned them down, according to The Sun.
The broadcaster hosted his last ever morning show on the station after eight years in September, with Nick Grimshaw taking over the slot.
Moyles was apparently offered a Monday to Thursday 10pm slot, but he was not interested. Phil Taggart and Alice Levine will host a new programme in the slot from January 7.
He was also given the option of presenting a weekend show, but is unlikely to make a return to the station.
Further talks will be held in January, but Moyles is said to be looking into the idea of setting up a 'new media' company in order to broadcast to fans.
A source said: "Radio 1 wanted Chris to do that show but he didn't want to. They hoped they could change his mind as they would like to have at least a fraction of the audience of eight million who tuned in to his Breakfast Show.
"He's now unlikely to stay with Radio 1 or indeed with BBC Radio.
"He is a massive geek and his head is full of ideas about how to broadcast to his fans without using traditional means. It's early days, but it's expected to be a digital proposition for the smartphone generation."
Chris Moyles said last month that he missed his Radio 1 team, but that he was "having a ball" with other projects.
Photo gallery - Chris Moyles's career in pictures:
Copyright: Rex Features