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6/1/2014 1:47 P.M. ET

Kluber closes book on sterling May

CLEVELAND -- Although he might not act like it, Corey Kluber's last month on the mound has produced remarkable results and likely thrust him into consideration for the All-Star Game.

In his six May starts, Kluber went 4-0 with a 2.09 ERA, giving up no more than three runs in any of those outings. Among 16 players with at least 37 innings pitched in May, his ERA was second only to the Yankees' Masahiro Tanaka (1.88), and his 60 strikeouts led all American League pitchers.

But there is little secret to Kluber's success: The steadiness of his mental approach combined with the rigor of his off-day routines are what have the right-hander among the best arms going this season.

"He's like a robot," Indians pitching coach Mickey Callaway said. "He's the same guy every single day, whether he pitches good or bad. There's no peaks or valleys. He's consistent and he does his work probably better than everybody."

Of course, Kluber's overwhelming arsenal of pitches has certainly helped his cause. With impressive movement on his sinker, cutter, slider and changeup, the 28-year-old has been able to keep hitters off-balance at the plate.

"He's cutting the ball at 91 [mph], sinking it at 96, got a devastating breaking ball, good changeup. He attacks hitters and moves the ball around, so hitters are never comfortable. He's not afraid to pitch inside," reliever Cody Allen said. "It's pretty fun as a reliever to come in after him because hitters just aren't that comfortable at all in the box."

Entering Sunday's action, Kluber led the AL with 95 punchouts and 10.7 strikeouts per nine innings. His 60 May strikeouts were the most by a Cleveland pitcher since Dennis Eckersley in 1976. He joins Yu Darvish as the only pitcher with 60-plus whiffs in a single month in the past decade, and his six consecutive starts with at least 6 2/3 innings pitched and eight strikeouts tied an Indians record.

But Kluber hardly takes the time to relish in his accomplishments. In fact, he consistently deflects praise away from himself and towards teammates.

"I'm just trying to go out and pitch a good game and give our team a chance to win each time out," Kluber said after his last start.

And apparently, that's just how the reliable righty prefers to operate. When he's not on the hill, he's out of the spotlight.

"He's very to himself, a pretty humble guy," Allen said. "He just had a pretty incredible month. He deserves all the praise, but he's not the guy that's going to take it. Pretty laid back, easygoing guy."

Chisenhall finding role, thriving for Tribe

CLEVELAND -- Lonnie Chisenhall entered this season unsure about what his role would be with the Indians. He knew manager Terry Francona would work him into the lineup, but there was little clarity and certainly no guarantees when it came to the frequency of at-bats.

Chisenhall decided to put the questions to the side and embrace each game that included his name on the lineup sheet. As the calendar flips to June, he has become a regular part of the lineup as a part-timer at third base, designated hitter and, more recently, first base.

"It's nice, because I feel like I've earned it. That was the big goal," Chisenhall said. "Last year it was a little different. They told me I was the third baseman out of spring. This year, it feels different. Nothing was given to me this year. I was coming in without a title.

"Now, it's just a good feeling knowing that what I'm doing on the field is helping make the decision harder on them every day. It's been good so far."

Heading into Sunday's game with the Rockies, Chisenhall had an impressive .369/.424/.554 slash line to go along with three home runs, 15 doubles, 15 RBIs and 22 runs in 43 games (130 at-bats). Most of the lefty-swinging corner infielder's at-bats have come against right-handed pitching, but Chisenhall has been earning more time against lefties, too.

Chisenhall thrived last September, when Francona limited him to one at-bat against a lefty. Chisenhall excelled this April, when he again was restricted to one at-bat off a southpaw. He was recently allowed to start two games against a lefty (Monday versus Jose Quintana in Chicago and Saturday versus Colorado's Franklin Morales) and is now hitting .563 (9-for-16) against left-handers this year.

Entering this season, Chisenhall hit just .194 in 124 at-bats off lefties across the 2011-13 seasons.

Chisenhall believes the strong showing so far off lefties is the result of work he has put in behind the scenes with hitting coach Ty Van Burkleo, who throws from the left side.

"I'm happy," Chisenhall said, "because the work I put in starting September of last year ... that's kind of been the whole process leading up to it. Just to have success and have it early, it's definitely reassuring."

Santana, McAllister nearing returns

CLEVELAND -- Two injured members of the Tribe could be back on the field sooner rather than later.

Carlos Santana landed on the 7-day concussion disabled list on Tuesday after experiencing a headache and dizziness earlier in the week. However, Santana could be back in the Tribe lineup by the end of the week.

Indians manager Terry Francona told reporters that Santana continues to feel better and that he could begin hitting off a tee and taking dry swings as early as Sunday.

"Carlos seems to think that he can play Wednesday," Francona said. "I think the training staff thinks Friday is a little more realistic. But the fact that he feels that strongly about it is really good."

Cleveland's skipper also noted that Santana, batting just .159 with six home runs this season, will have to keep progressing through his rehab activities without showing any of his concussion-like symptoms if he wants to return this week.

Meanwhile, right-handed pitcher Zach McAllister (back) is expected to make a rehab start on Wednesday with Class A Lake County. He threw a brief bullpen session on Sunday.

"He's fine," Francona said. "He's all set to go. He'll get two days off and then go pitch."

Francona also mentioned that the Indians will wait to decide if McAllister needs another Minor League outing under his belt until they see him pitch on Wednesday.

"Don't think there's going to be a whole lot of buildup, but I think we'd like to see how he does," he said.

McAllister went 0-2 with a 10.67 ERA in his last four starts before being hitting the 15-day disabled list on May 22.

Quote to note

"He's just doing everything. He got a bunt down [on Saturday]. He's just playing the game. That's what he's doing. He's just playing the game really well. And then you add on to that, you can move him from third to first in a one-run game or a tie game, and not even think anything of it. That's quite an accomplishment on his part."
--Indians manager Terry Francona, on Lonnie Chisenhall

Smoke signals

• Indians lefty Michael Brantley went 0-for-4 on Saturday, ending a 15-game hitting streak overall and a team-record 19-game hitting streak at Progressive Field. The home hitting streak record for an Indians batter at Cleveland Municipal Stadium was 27 (Miguel Dilone iin 1980) and the mark for a Tribe hitter at League Park was 30 (Hal Trosky in 1936).

• For the month of May, the Indians ranked in the top three as a team in the American League in average (.273), on-base percentage (.344), slugging percentage (.428), OPS (.772), runs (136), doubles (56), walks (102) and fewest strikeouts (183). Cleveland led the league last month in OBP, was second in OPS and tied for third in the AL in runs scored.

• Class A Lake County infielder Paul Hendrix entered Sunday ranked sixth in all Class A levels combined with a .342 average on the season. Hendrix (selected in the 18th round of the 2013 First-Year Player Draft) was third in all of Minor League baseball with a .413 average since May 8, when he recorded his first career four-hit game.

• Johnny Football is getting ready to pick up a baseball. On Wednesday, Browns rookie quarterback Johnny Manziel and fellow first-round pick cornerback Justin Gilbert will throw out ceremonial first pitches prior to Wednesday's game against the Red Sox. New Browns running back Ben Tate will do the honors before Tuesday's game.

Jordan Bastian is a reporter for MLB.com. Read his blog, Major League Bastian, and follow him on Twitter @MLBastian. Alec Shirkey is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.