The actress is such a huge fan of the musical TV show she has spent hours creating her own character which she thinks writer Ryan Murphy should consider including in the series.
The character the Hollywood star has devised would be the lesbian aunt of gay student Kurt Hummel - who is played by Chris Colfer.
Appearing on 'Late Night with Jimmy Fallon' on Thursday (18.11.10), she revealed: "I would love to be on 'Glee'. Can I make a confession? In my head I've written a part for myself in 'Glee'! It's so arrogant and obnoxious, it's like, 'Ryan Murphy no one else wants to be on your show.' But in my head I've cast myself and I know which song I'd sing. I would want to play Kurt's long-lost aunt, his mother's sister who is also gay, who comes back to help him deal with his sexuality and I would sing 'No One Is Alone' from Stephen Sondheim's epic show 'Into the Woods'."
If the creators of 'Glee' do decide to take up Anne's story idea, she would not be the first big name star to get a cameo.
Gwyneth Paltrow appeared as a Spanish substitute teacher in the episode which aired in the US this week and will be a short-term character, while Britney Spears had a brief appearance in a show dedicated to her during the current season.