The character, who features heavily in author JRR Tolkien's most famous works The Hobbit and The Lord of the Rings, has been made famous by veteran actor Ian McKellen in Peter Jackson's screen adaptations.
McAvoy, 33, said that he would like the role should there be any prequels to the recent films, reported Digital Spy online.
Revealing an in-depth knowledge of Tolkien's work, he specifically referenced the possibility of appearing in something adapted from Tolkien anthology 'The Silmarillion'.
"It's a collection of poems and songs that chart the ancient history of Middle-earth. My true geek is coming to the fore, but they're really, really beautiful stories.
"In part of that is the genesis of Gandalf, or Mithrandir, or Stormcrow, or any of his many, many names. Anyway, maybe that's the one," said McAvoy.
"The Hobbit: An Unexpected Journey" is currently at the top of the UK box office, and set a December box office record in the US.