Veteran Fernando Rodney will get first crack at the ninth-inning role based on experience and past performance, but youthful candidates such as Kevin Jepsen, Jordan Walden and Michael Kohn are in the wings.
Rodriguez, 28 and brimming with confidence and good cheer, would like to toss his hat in that ring.
"I was 10-for-10 closing games in the Mexican Pacific League this winter," Rodriguez said. "I've never been a closer before, but I liked it. I think I've got pretty good stuff. I hit 97 [mph] a couple times, 98 two or three times. I was hitting 94 pretty consistently.
"I'm still working with a two-seamer and cutter. Sometimes I flip over a curveball. I got a few strikeouts with it in winter ball."
In 43 appearances for the Angels last year, Rodriguez delivered 47 1/3 innings and a 4.37 ERA. He had 36 strikeouts while walking 26 and giving up 46 hits.
Rodriguez had a dazzling beginning. In his big league debut, at Yankee Stadium of all places, he worked a scoreless inning with a strikeout on April 15.
Through his first seven appearances, he hadn't allowed a run with 11 strikeouts while yielding three hits and no walks.
"He has back-end-of-the-bullpen stuff," Angels manager Mike Scioscia said of the Mexicali native. "He's got a power arm, and he's fearless. He was real consistent when he came up.
"The internal competition just to make our club is strong. Once guys make the club, there's another competition for roles. Francisco is in the same spot as Michael Kohn, Rich Thompson, guys trying to carve roles on our club."
Rodriguez's fate rests in his ability to refine, adjust and think his way through rough patches.
"In the Major Leagues, he tried to throw through trouble rather than pitch through trouble," Scioscia said. "Some things have gotten away from him when he has to understand how to make pitches to get out of trouble. Instead of pitching at 93, he tries to pitch at 96, which is counterproductive."
Rodriguez understands he needs to temper his enthusiasm and learn to control the adrenaline. It's his main focus this spring.
"I'm kind of a hyper guy, all over the place," Rodriguez said. "I have to use my adrenaline and aggression and learn how to make it work for me.
"The thing I learned last year is that I can compete here; I'm ready for this level. There is good competition here, and personally, I like to be around good pitchers. There's a lot of experienced guys and young guys here.
"At the end of the day, you compete with yourself -- not the rest of the guys."
Rodriguez is self-educated, an avid reader -- "philosophy, psychology, chemistry, math, anything I can get my hands on. I love to read.
"Anything I can find to help me get better, that's what I want to read."
The book on hitters when he reached the big leagues was full of warnings.
"I faced some really good hitters, like Manny [Ramirez], [Dustin] Pedroia, [Paul] Konerko," Rodriguez said. "Manny got a ground-ball single with the infield shallow. I struck out Pedroia, and Konerko flied out to center field."
Elvis Andrus and Michael Young of the Rangers both were 0-for-4 against Rodriguez, but Vladimir Guerrero was 2-for-4 with a homer and Josh Hamilton was 2-for-3 with a double.
Ichiro Suzuki was hitless in three at-bats against Rodriguez, and Derek Jeter was 0-for-2.
Five rocky outings out of 43 elevated his ERA, but that's how it goes with relievers. All in all, the second Francisco Rodriguez, from down Mexico way, was one of the club's bright spots in a dismal 2010 season.