The acclaimed British actor has appeared as the Hogwarts professor turned headmaster in all eight films of the series based on JK Rowling's best-selling novels.
Radcliffe recently described Harry Potter and the Deathly Hallows: Part 2 as being "pretty spectacular", while acknowledging Rickman's "stunning" final outing as Snape as being "quite possibly the film performance of his career".
"The performance that I found most moving was Alan Rickman," Radcliffe said. "I've said this in interviews a lot recently, and I'll keep saying it, because I do think it's the film performance of his career.
"I think he should get nominations for 'Best Supporting Actor', because I just think... it's so touching and heart-wrenching and beautiful what he does. I'm really thrilled to share the screen with him."
Harry Potter and the Deathly Hallows: Part 2 opens in cinemas next Friday, July 15.
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Watch Hollywood stars including Tom Hanks, Ryan Reynolds and Vanessa Hudgens offer their thoughts on the end of Harry Potter: