But there's one moniker that escapes Miller's grasp, one that he'll be chasing for at least a decade longer.
"I don't have any control over that, what people say, what people think," Miller told reporters Thursday, per ESPN. "But I want to be the best player in the National Football League. That's what I go out there to be every time I play. ... Over time, my play and the type of person I am will speak more to that. Maybe when I'm done, after playing 17 years or whatever, we can revisit this and see.
"I want to be the best player, no question. I want to be a G.O.A.T.-type player, like the guy upstairs."
As long as Brady is still slinging it in Foxborough, and according to the QB that could last until the mid-2020s, Miller will have to contend with him, and every other future Hall of Fame passer for G.O.A.T. status. It's just the nature of the debate: All quarterbacks earn more attention and adulation, warranted or not, before, during and after their careers than other position players.
One step Miller can take this season on his long path toward goat-ness is reaching the peaks of his earlier seasons -- Miller tallied 18.5 sacks in 2012 prior to tearing his ACL the next year -- when he wasn't the poster child for Old Spice or Madden or Dancing With the Stars.
Miller suggested to reporters that, free of a demanding offseason of non-football obligations in 2017, he can "push my body to a spot where it's never been before. You're never guaranteed that working hard will translate to on-the-field success, but that's what I'm hoping for."
With DeMarcus Ware put out to pasture and a new coach and defensive coordinator calling the shots in Denver, Miller will be looked at as the presumptive leader and fixture on the Broncos' defense this season. Leading a young front seven on a division-winning charge in the competitive AFC West surely wouldn't hurt his G.O.A.T. candidacy.