Minnesota (93-59) holds a four-game lead in American League Central over the Cleveland Indians (89-63) with 10 games to play.
Kansas City (56-97), which has lost five of its past six games, is in fourth place, 37 1/2 games behind the Twins. However, the Royals will have a big say in whether Minnesota can win its first division title since 2010. The teams finish the season with a three-game series in Kansas City next weekend.
Minnesota is 9-3 this season against the Royals and has swept two of the four series the teams have played.
Gibson will be making his second start and third appearance since returning from a 12-day stint on the injured list caused by ulcerative colitis, a condition that saw him lose 10 pounds over a six-week period and also made it difficult for him to sleep.
Most recently, Gibson allowed two runs (one earned) in one inning of relief work at Cleveland on Sunday.
He is 9-5 with a 3.55 ERA in 21 career starts against Kansas City, including 2-0 with a 3.26 ERA in three starts this season.
Montgomery is just 1-5 with a 7.85 ERA in 17 road outings (five starts) this season but is 1-0 with a 2.77 ERA in three career appearances (two starts) against the Twins.
Both teams come in off poor offensive performances in losses on Wednesday.
Minnesota was no-hit for 5 1/3 innings and finished with just three hits against eight Chicago White Sox pitchers in a 3-1 loss. Kansas City, meanwhile, managed only four hits in a 1-0 loss at Oakland that ended on Mark Canha's two-out, walk-off double in the 11th inning.
"We're trying to play every team like that right now," Royals left fielder Alex Gordon told MLB.com. "We have a lot of young guys here trying to get experience and trying to improve so we can have a better year next year."
"We were going at 'em, man," added Royals starter Danny Duffy, who allowed just two hits and a walk over seven scoreless innings while striking out six. "The team did a really good job of matching that intensity. Overall, you're never happy coming out on the losing side, but we were pleased with our effort."
Minnesota leads the majors with a single-season record 289 home runs, one more than the New York Yankees, and is the first team in history to have five players with 30 or more home runs in a season. Nelson Cruz leads the way with 37, followed by Max Kepler (36), Eddie Rosario (31), Miguel Sano (30) and Mitch Garver (30).
Rosario had a double, Minnesota's lone extra-base hit, in the Wednesday loss. He also drove in a run with a single.
"It kind of shows you a little bit that sometimes these bullpen days can definitely be challenging to deal with," Twins manager Rocco Baldelli said of the White Sox's pitching parade. "We had our chances. We had some good pitches to hit. The at-bats were probably just OK today.
"It wasn't our best offensive night. That's definitely going to happen. Our offense has been consistently good this year. Tonight was just one of those nights."
--Field Level Media