Rodriguez is considered by MLB.com Draft expert Jonathan Mayo as the prospect most likely to first arrive in the big leagues after Blue Jays first-round selection Marcus Stroman.
Rodriguez is the sort of polished veteran college pitcher that can jump into professional baseball and move up the ranks faster than most, White said.
The 6-foot-3, 225-pound lefty, a native of Miami, has been one of the University of Florida's most reliable pitchers this year, posting a 3-2 record with four saves and a 2.08 ERA. He has struck out 79 batters in 60 2/3 innings.
Rodriguez and his college coaches were unavailable for comment on Tuesday as the Gators are preparing for the Super Regionals against N.C. State beginning Saturday.
"He pitches at a good program in Florida, and they've got a really good staff," White said. "He's thrown a number of innings out of that bullpen, and you're talking about a guy who is deceptive and he's got a power arm."
He throws in the 90-94-mph range and he has a nice breaking ball as well. White said he's simply the sort of pitcher that throws a lot of strikes and competes.
The lefty has struck out 79 batters in 60 2/3 innings this season. He was drafted by the Astros in the 48th round in the 2009 Draft, but opted to go to Florida, where he dominated out of the bullpen.
The Dodgers approached the Draft valuing lefties over any other position -- despite wanting to always go with the best available player -- and they got their man in Rodriguez.
White emphasized that Rodriguez has the ability to get both righties and lefties out thanks to his delivery and size. Closing is a possibility down the road and so is starting, but Los Angeles is going to leave Rodriguez in the bullpen for the time being and let him continue to grow from there.
However, with how polished Rodriguez already is, that may not be long.
"As soon as he's ready and as soon as we need him, if we need him, I think he can be more than a left-on-left guy," White said. "I don't see why he doesn't have the stuff to pitch in any role you want out of the bullpen."