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6/10/2014 6:46 P.M. ET

Chisenhall overwhelmed by flurry of attention

KANSAS CITY -- Lonnie Chisenhall had no time to enjoy his newly acquired rock-star status.

A day after he entered baseball lore for Monday's 5-for-5, three-homer, nine-RBI performance against the Rangers, the Indians third baseman became consumed in a whirlwind of media requests and congratulations from friends and family.

Most notably, Cooperstown contacted Chisenhall on Tuesday asking for the bat he used against Texas. Chisenhall agreed to donate it to the Hall of Fame.

"If they're going to call and ask for it, they can have it," Chisenhall said, who only brought two bats on the current 10-game road trip and will have to borrow lumber from teammate Michael Brantley -- and possibly others -- until a new shipment arrives in Boston.

"Sometimes you have to give up a piece that maybe means something to you to give it to the game and I'm all for it," Chisenhall said.

Instead of basking in his own glory, Chisenhall spent Tuesday fielding numerous media requests and hearing from friends and family.

"I'm getting pulled in a lot of different directions, and I'm just trying to handle it the best way I can," Chisenhall said. "I'm not used to the amount of text messages and interview requests and things like that."

Chisenhall tried to accommodate all, but this task proved impossible.

"I've never had to turn down an interview before, and that was the case today. I did as much as I could, but at least it's all positive," Chisenhall said. "I'd have a hard time if it was something negative [that] I'd have to be answering so many questions about."

McAllister closer to returning to action

KANSAS CITY -- Zach McAllister made a successful rehab start Tuesday, and the Indians starter looks poised to join the team soon.

McAllister, who went on the disabled list May 22 with a strained lower back, pitched six innings at Triple-A Columbus, allowing two runs and three hits, while striking out six.

"It sounds like, as the game went [along], he started to throwing better, which is a good sign," Indians manager Terry Francona said. "Nothing came from medical, [there weren't] any red flags or anything, I think he did fine."

Francona said McAllister will fly into Boston for the Indians' next series, at which point, McAllister, Francona and his staff will work out a plan to ease him back into action.

"We'll sit with him, and we want to work through where we want to insert him, where it best suits us," Francona said. "We've got, obviously, a few things to look at. We spent some time on it today, and we'll continue to and then we'll figure it out."

McAllister struggled in first 10 starts of the season, posting a 5.89 ERA in 47 1/3 innings.

Indians reach terms with several Draft selections

KANSAS CITY -- The Indians announced Tuesday that they have signed four of the players selected in the 2014 First-Year Player Draft. Cleveland agreed to terms with college draftees Julian Merryweather, Steven Patterson, Austin Fisher and J.P. Feyereisen.

Merryweather, the highest draftee of the bunch, was selected in the fifth round out of Oklahoma Baptist University. Merryweather, a right-handed pitcher, logged a 12-3 record and a 1.07 ERA as a senior. Merryweather held opponents to a .181 batting average and struck out 132 batters this season.

Patterson, a 10th-round selection, was taken out of the University of California-Davis. The infielder was named Second Team of the All Big West conference as a junior. Patterson batted .326 with one home run and 24 RBIs as a senior, and he walked 21 times in 41 games this season.

The Indians also signed Fisher, a 13th-round selection, and Feyereisen, who was taken in the 16th round. Fisher, an infielder, was drafted out of Kansas State University. Feyereisen, a 21-year-old right-handed pitcher, was drafted out of the University of Wisconsin at Stevens Point.

After coming to terms with the four draftees earlier in the day, the Indians continued with signing Grant Hockin, their second-round pick.

Cleveland gave Hockin, a right-handed high school pitcher, a $1.1 million signing bonus Tuesday, according to MLB Network analyst Jim Callis.

That exceeds the $928,700 the Indians' second-round pick was valued for.

The Indians have not confirmed the Hockin signing.

Smoke signals

• Indians farm hand Claudio Bautista (Class-A Lake County) was named the team's Minor League player of the week for June 2-8. The second baseman picked up the award behind the strength of an 8-for-21 week that included two doubles and three home runs in six games.

Jackson Alexander is an associate reporter for MLB.com. Spencer Fordin is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.