Kennedy's spot in the rotation will come up again on Tuesday against the Rays at Tropicana Field. As of now, Yost said he is leaning toward right-hander Chris Young to make that start.
"There are a number of things we can do," Yost said. "It could be Woody [Travis Wood] or CY. Not really considering [Mike Minor].
"I'm leaning right now toward CY. He could get us through five."
Kennedy sustained a Grade 1 strain of the right medial hamstring on Thursday during the fifth inning of an 8-3 loss to the White Sox. He'll have to miss at least two starts.
"I'll try to do my best for these 10 days to get ready," Kennedy said. "They don't want this to be a nagging thing for a month or so, so the smartest thing is to get the inflammatory medicine in there and get it healed."
Almonte, 24, had been one of the Royals' top pitching prospects for years, but he is now ranked 16th on the team's overall list by MLBPipeline.com. He posted a 5.40 ERA in 2015 at Triple-A Omaha. And last year, Almonte, after a rough start at Omaha (5.55 ERA), was demoted to Double-A Northwest Arkansas and made all 11 appearances there out of the bullpen.
This year, Almonte made two adjustments: He began working out of the stretch almost exclusively and he also got taller in his delivery, creating more of a downward action on his pitches.
The adjustments have worked: In five appearances (four starts) this season at Northwest Arkansas, Almonte has posted a 1.85 ERA and a 0.86 WHIP. He has held opponents to a .186 batting average.
"On one end, I'm really happy [to get called up]," Almonte said through interpreter Pedro Grifol. "But on the other end, I'm coming up because someone got hurt."
Young said he'll be ready if he gets the call. He said he's not concerned about what it will take to get stretched out as a starter, or having a pitch count if he gets a start.
"I'm not going to put a number on it," Young said. "It's just whatever it takes."