Count Cleveland's David Huff among them.
The Indians left-hander has made just two starts this season after being called up earlier this month. If he can turn in one or more outings like he did last time against the Royals, he might be able to put himself into consideration for next season's rotation.
On Sunday, Huff worked 5 2/3 innings, but he limited the Royals to just one run on three hits and a walk. He picked up the win, his second of the season in four appearances.
"I really just want to finish strong," Huff said. "Put my name out there because I know at the beginning of the year and throughout the year, they probably wrote me off. Ultimately, after the injury and everything, getting back to the way I was. It's been a long grind, and I'm just trying to finish strong."
Huff gets a rematch with the Royals in Friday's series opener at Progressive Field, and he'll look to continue the kind of pitching that's seen him allow just four runs in 16 innings. However, it'll be without Manny Acta on the Indians' bench. The team announced on Thursday that Acta would not return as skipper in 2013 and that Sandy Alomar would manage the club for its final six contests this season.
Meanwhile, the Royals will send rookie left-hander Will Smith to the hill. Smith picked up his sixth win of the season his last time out against the Tribe, allowing two runs over seven innings.
He's 2-0 against the Indians this season, allowing up a total of four runs in 13 innings and is 2-2 in September with a 3.24 ERA.
"I know I beat 'em for my first victory, but they're just like any other team," Smith said. "They're Major League hitters, they're good hitters. You still have to execute your plan, attack 'em, put up zeros and give your team a chance to win."
Royals: Gordon gets past half-century mark
Royals left fielder Alex Gordon banged his 50th and 51st doubles in Wednesday night's 5-4 loss to the Tigers, marking the second highest number in Royals history.
While he went 0-for-4 in Thursday's contest against the Tigers, Gordon is just three doubles shy of Hal McRae's club record of 54 in 1977.
"It's pretty cool," Gordon said. "Any time you get a career high in something when you've been playing for a while, it's pretty special."
Indians: Ubaldo done for year
Starter Ubaldo Jimenez will miss his final start with a right ankle sprain. He had his ankle examined in Cleveland earlier this week after experiencing symptoms in each of his last two starts.
Right-hander Roberto Hernandez threw four innings and 60 pitches in a simulated game on Wednesday in Chicago. His status for one more start this season has not been determined.
In 28 career games against Kansas City, Indians catcher Carlos Santana is batting .320 with six home runs and 24 RBIs. He's walked 21 times, compared to just 17 strikeouts. He hit two home runs and drove in a career-high five runs on Sunday at Kauffman Stadium.
Billy Butler is hitting .357 in 14 career at-bats against Huff. That includes two doubles and three RBIs.