"He's healing very well," Esposito told E! News at the premiere of "The Jungle Book," in which he voices Akela. "He got put together a couple of weeks ago ... He's one tough cookie."
Esposito added that O'Brien is expected to recover enough to return to filming "The Maze Runner: Death Cure" on May 15.
A safety report seems to indicate O'Brien suffered a "concussion, facial fracture and lacerations" after falling off a motorcycle that went into a slide after a stunt.
"He got his bell rung. I would imagine many who witnessed thought that was it ... [But] he's a survivor," Esposito said. The one good thing about Dylan that I think is going to help him get back on schedule with us very soon is he has a great attitude."
"The Maze Runner: Death Cure" is the third film in the franchise, based on the popular dystopian YA novels. O'Brien also stars in MTV's "Teen Wolf."
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