Kela has been on the disabled list retroactive to June 30 with a sore right shoulder and is scheduled to throw in the bullpen for a second time on Tuesday. If that goes well, the Rangers will then decide if he is ready to be activated or needs at least one outing in the Minor Leagues on a medical rehabilitation assignment.
"Everything is predicated on getting through his throwing program," manager Jeff Banister said.
Diekman had his third and final surgery on June 9 and has been throwing on flat ground for a month. He stepped on a mound for the first time on Monday, just to throw eight light tosses and get used to the slope of the hill. He gets full clearance to throw a full mound session on Thursday, and that will be a big day for the lefty.
"I feel really good," Diekman said.
Diekman has been able to keep his arm in reasonable shape while undergoing surgery for ulcerative colitis. He doesn't expect any issues with the rest of his body.
There is no timetable on how long it will take Diekman to get ready to pitch in a Major League game, but his goal is to return for the final two months of the regular season and another month of postseason.
"If I can't throw for three months after a full month of throwing, I don't know what I'm doing here," Diekman said.
Griffin has been out since May 27 with a strained left intercostal muscle and threw three scoreless innings in a Rookie League game in Arizona on Friday. He is penciled in for four innings and 60 pitches on Thursday for Round Rock.
• Mike Napoli hit a home run in two of three games in Kansas City, but was on the bench Monday with right-hander Chris Tillman pitching for the Orioles. Joey Gallo was at first base and Banister said, "It was a tough decision. Napoli is swinging the bat well. I've seen when Napoli gets hot, he can run the table. I don't see that as a platoon."
• Alex Claudio pitched a scoreless inning in each of his three appearances in Kansas City and did so in eight pitches or less each time. That's a first for Rangers pitchers since pitch counts started being tracked in 1988. He averages 12.6 pitches per inning, the lowest for an American League reliever.