Farnsworth was scratched from his scheduled road appearance against the Twins on Tuesday and did not make the trip with the Rays from Port Charlotte.
No roster move has been made, but one is expected before Wednesday's 5 p.m. ET deadline for all big league rosters to be set.
"Kyle's experiencing a sore elbow, so we had to have him checked out," manager Joe Maddon said. "We're going to have to wait on making a specific move for him yet ... If [a DL move] in fact does happen, we will have to try to figure out the ninth. I'm not going to try to proclaim anybody, we will just continue to deal with that."
Farnsworth has been sore "off and on," Maddon said, but the team believed it was something Farnsworth could work through. Farnsworth had elbow trouble at the end of the 2011 season and turns 36 in 11 days.
Farnsworth last pitched in a Grapefruit League game Saturday against the Red Sox, allowing a run on two hits in an inning of work with one strikeout. That was the only run Farnsworth gave up in five appearances and 5 1/3 innings this spring. He gave up six hits, walked none and struck out two.
"On that day, [he] still got the ball up to 95 mph, his slider was up a little bit, I just thought, we thought, he wasn't finishing his pitches that well," Maddon said. "So, we talked to him about it. We had him checked out, and so we have a little bit of an issue, that's all. All the work was done on it."
Rodney, a right-hander, returned to game action on Tuesday, six days after a line drive caught him on his throwing forearm last week. He threw a scoreless inning, with one baserunner allowed on a walk, and said afterward he felt good.
"I saw no ill effects," Maddon said. "His arm looked very loose. If you watch him throw, this guy's got a real loose arm and it was in the warmups, and then the ball came out 95. And I know he has more in the tank than what we saw today, but I liked what I saw."
Rodney's given up two runs in 7 1/3 innings this spring for a 2.45 ERA, striking out four and walking five. The 35-year-old right-hander has 87 saves in nine big league seasons, with a career-high 37 coming with the Tigers in 2009.
"Whatever they need, I try to do my job, help my team," Rodney said. "I think I have a little bit of experience [closing]."
Peralta, 36, stepped in for Farnsworth late in 2011 and saved six games. He's given up five runs in 8 2/3 innings this spring for a 5.19 ERA, with 14 strikeouts and two walks.
"He did a great job and Rodney's done it before and I think there's a few other guys that can do it if they're asked to," Rays starter Jeremy Hellickson said of his confidence in the bullpen if Farnsworth is out. "But we want Farnsy back there."