The comic is a big fan of the sci-fi show and joked that he would be willing to take any part, no matter how small.
"I asked my manager to get me a part in Doctor Who. I didn't need a big part - a monster or a lunar rock - but I would love to be able to tell my grandchildren I was in it," he told The Graham Norton Show.
"My manager said, 'I'm sure it won't be a problem'. He got in touch and got an email back that said, 'We are really happy that it is something Frank would like to do…' Somehow the end of the email seemed to have been cut off..."
Former Doctor Who actress Billie Piper is also on this week's Graham Norton Show and Skinner confessed that he had accidentally called her by her character name 'Rose' when he met her backstage before the show.
The Graham Norton Show airs this Friday (January 4) on BBC One.
Josh Groban and Example are the other guests on the chatshow this week.