Wright is dealing with a strained oblique muscle in his left side and that might put him on the DL.
"If he is going to be [sidelined] a bunch of days, then we'll have to make a move in that direction," manager Ron Washington said.
If the Rangers think that Wright will be available soon, then they will give strong consideration to sending down Fukumori. He has made three appearances for the Rangers and allowed six hits and four walks in just 1 2/3 innings.
He underwent right elbow surgery last summer and missed the second half of last season. It's apparent that he could use more time to regain his effectiveness. He and Josh Rupe are the only two relievers -- besides closer C.J. Wilson -- with options.
Dustin Nippert was a candidate to go on the DL because of a sore left shin, but that option seemed to vanish when he threw 2 2/3 scoreless innings against the Blue Jays on Friday.
"He threw the ball extremely well," Washington said.
Guardado said that he's been dealing with inflammation and discomfort in his shoulder since the Rangers returned to Texas from their season-opening road trip. He also revealed that he has been dealing with a tear in the front of his rotator cuff for the past five years, but said that has nothing to do with this injury.
"I probably just irritated it, that's all I can say," Guardado said. "I've felt a pinch there before, so this is nothing new. It's not fun at all, because I was right where I wanted to be."
Guardado sat a whole year because of Tommy John elbow reconstruction surgery before returning last August. The Rangers signed him as a free agent in the offseason.
"It's frustrating to come so far from last year to where you want to be," Guardado said. "I'll be fine. I just have to get it right. I just don't want to do anything stupid like I always do. I'm a little smarter and wiser now."
Guardado's absence leaves the Rangers without a left-handed reliever other than Wilson. It's a reminder that the Rangers miss John Rheinecker, who was a potential left-handed setup reliever for them until he underwent shoulder surgery in Spring Training. He is sidelined until the All-Star break.
Instead the Rangers are left with six right-handed relievers behind Wilson: Joaquin Benoit, Franklyn German, Nippert, Rupe, Wright and Fukumori.
"You'd like to have that extra left-hander, but we'll just have to make that adjustment," Washington said. "There are some ballclubs without one, but you'd like to have one."