On Wednesday, McShay also moved Louisville quarterback Lamar Jackson into Round 1 in his "3.0" mock. The 2016 Heisman Trophy winner landed with the New Orleans Saints at No. 27.
The draft analyst has remained consistent, keeping Darnold in the top spot for each of his three mocks.
While Ian Rapoport of the NFL Network reported Penn State running back Saquon Barkley is "firmly in the mix" for the Browns at No. 1 after his dominant showing at the 2018 NFL Scouting Combine, McShay believes Cleveland will go QB unless it addresses the position in free agency.
Meanwhile, Darnold discussed potentially joining the Browns during his combine media session.
"I think if Cleveland takes me No. 1 it would be great opportunity, first of all," he told reporters. "That goes for anyone taking me at any position. Honestly, it's always been a dream of mine to play in the NFL. And I think turning a franchise around is obviously a hard thing to do. But I'm always accepting of a challenge. And I think it would be an amazing thing to do."
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Jackson has been one of the most talked-about prospects in the class. Amid speculation that some teams would prefer he switch to wide receiver, the Cardinals standout made it clear at the combine he has no plans to do so.
"That's crazy," he said. "I thought I did a good job at quarterback. I thought I did. You know? But, hey, they say what they want to say. I'm here now. I'm happy to be here. Now I just have to show my ability."
Longtime Saints quarterback Drew Brees is a free agent this offseason, but there's been no suggestion he'll leave the franchise. General manager Mickey Loomis said both sides are fully intent on getting a new deal done, per Herbie Teope of the Times-Picayune.
Nevertheless, Brees is 39, so it would make sense to think about drafting a QB of the future.