But had he been, Bruins coach Jim Mora believes his quarterback would have been chosen No. 1 overall.
"In my opinion he (would have been) the best quarterback in the draft and he would've gone first," Mora told The Rich Eisen Show on Friday.
Rosen was outstanding last season as a freshman, passing for 3,670 yards and 23 touchdowns with 11 interceptions. He arrived at UCLA as a highly touted recruit, and won the starting job as the immediate successor to Brett Hundley. NFL Media analyst Chad Reuter ranked Rosen as the No. 9 player in the college game earlier this month.
Still, with most of his college eligibility still ahead of him, Mora believes Rosen has plenty of work to put in.
"I'm going to say (he would've been picked first) publicly because I believe it, but with this disclaimer: Unless he continues to work hard, unless he makes good decisions, unless he dedicates himself the way guys like Tom Brady and Drew Brees and Peyton Manning have, then it's a pipe dream," Mora said. "And I've asked him this. I said 'Who do you want to be? Do you want to be Johnny Manziel or do you want to be Tom Brady? And you need to make that decision right now and you need to start working in the direction that you want to work in.'"
Rosen's first opportunity to enter the draft won't come until 2018, if he chooses to apply for early eligibility as an underclassman, or in 2019 as a senior. While Rosen's prolific talent was readily apparent even as a freshman, he'll face a significant challenge as a sophomore with the departures of four offensive weapons chosen in the 2016 draft: RB Paul Perkins, TE Thomas Duarte, WR Devin Fuller and WR Jordan Payton.