McAvoy's Star Trek parody, titled Star Force: Sci-Fisolation, is filmed entirely from home using regular everyday objects.
The series has led to fans wondering if McAvoy is open to portraying a young Jean-Luc Picard, a Star Trek role held by Patrick Stewart. McAvoy already has a history of playing a younger version of Stewart in the X-Men film series.
"Is there any world where you would play a young Jean-Luc Picard?" host Jimmy Fallon asked the actor on Wednesday.
"Jimmy, that is the only world that exists in which I will play Jean-Luc Picard. Any other world is just an alternate reality in a bad episode of Star Trek," McAvoy responded.
McAvoy said that if he isn't hired, he will film himself as a young Jean-Luc Picard on his phone.
"I'm calling it right now. I'm doing the virtual lockdown equivalent of rubbing my scent all over Patrick's face and saying this territory is mine. All other bald actors can [expletive] off," he said.
McAvoy voices Morpheus in the audiobook adaptation of comic book series The Sandman which is available through Audible. McAvoy told Fallon that he had to make a studio in his home to record his lines.
"I think it's like a cast of a hundred or something. They had all recorded their stuff and I got to listen to every single episode and then lay down my stuff. So it was absolutely fantastic," McAvoy said.