The 'Glee' star was taken by his co-star Lea Michele took him to meet the singer at his Academy Awards party but felt awkward when he realised the 'Rocket Man' hitmaker was about to sit down to eat, so decided to take a humourous approach to their first meeting.
He told Maclean's magazine: "I asked him, 'Is there anything I can get you sir? Another beer?' Maybe I was too convincing, as he just said, 'No, thank you,' and never looked up from the chicken."
Embarrassed, Cory decided to try again, asking: "Are you sure? Some water, perhaps?" and received only a shake of the singer's head.
Cory who plays heartthrob Finn Hudson in the musical drama - eventually gave up his pretence and was introduced to Elton by Lea, but admits the meeting still didn't go the way he had hoped.
Cory explained: "He just gave me a 'what-the-hell' look, shook my hand and went back to his dinner. It was one of the most embarrassing experiences of my life."
Meanwhile, Lea - who plays Cory's on-screen girlfriend Rachel Berry in 'Glee' - has spoken about how comfortable the pair are working together after two series of the show.
She said: "We're such good friends that we've passed that level of weirdness. Cory farts in front of me."