But the five-star has his top choices all come from the Pac-12.
After attending a number of football camps over the summer including all four of those schools', Rosen said he doesn't have a favorite right now.
"Initially Stanford stood out, but I've started to take a few more visits," he said. "I've watched a bunch of UCLA and USC games and I have more of an open mind right now."
Rosen was at UCLA's game against Cal on Saturday, seeing two of his top four teams.
On the season, Rosen is having a good year, despite missing a couple of games with injuries.
In the first six games of the 2013 season, St. John Bosco has outscored its opponents 295 to 95 and continued its undefeated streak with a 56-12 win over Trinity League rival Santa Margarita on Oct. 11. Rosen went 19-of-24 passing for 211 yards and one touchdown while running for 56 yards and four touchdowns.
"We threw when needed and did a really good job running the ball on the ground," Rosen said. "I think we carried our game plan really well and did what we needed to put points up."
Despite his impressive play and list of schools, Rosen insisted he isn't in a rush to commit and will wait to focus on all his offers at the end of the Braves' season.
"The recruiting process is just starting to get going but I just want to see how everything goes and most of all just focus on my season right now. I have a lot of time after the season to take care of all that."