Moyles has worked on a new programme about the history of the Radio 1 breakfast show, The Sun reports.
Former presenters including Tony Blackburn, Zoe Ball, Mike Read, Mike Smith, Simon Mayo and Sara Cox all agreed to sign up for the documentary.
However, Evans, who now hosts the Radio 2 breakfast show, has allegedly decided not to feature in the programme.
"Chris doesn't want to talk to us, which is a bit of a shame as his breakfast show was massive," Moyles said. "It kind of changed the way breakfast shows are done."
When Moyles Met The Radio 1 Breakfast DJs will air on Sunday, May 9 at 9pm on BBC Two as part of Radio 1 Night.