TVGuide.com said Bonneville is friends with Stones member Ronnie Wood and hopes the musicians will agree to guest star on his early 20th century-set series.
"Obviously, they wouldn't play themselves, but they could be a rag-tag bunch of traveling entertainers or even a circus act," a source told The Guardian. "It would be such a coup, and fun for the Stones. They really are huge fans of the show."
"Apparently, they were stopping rehearsals on Sunday nights in time to get back to watch it... When Sybil passed away, Mick [Jagger] said to Ronnie [Wood], 'Sad to hear about the girl.' Ronnie replied, 'I haven't seen it yet -- I recorded it,'"
"Abbey" cast member Laura Carmichael told the newspaper.
Celebrity Couples of 2014 [PHOTOS]