Manager Terry Francona said the club is optimistic that Bourn will be able to return by April 30, when he is first eligible for activation.
"That would be the hope," Francona said on Wednesday. "I bet you it'll be very close. That sounds about right."
Bourn, who signed a four-year, $48 million contract with the Indians in the offseason, sustained the injury sliding into first base on a grounder to the right side in the eighth inning of Sunday's game. On the play, Chicago pitcher Matt Thornton stepped on Bourn's hand while covering the bag. Bourn was safe, but he exited the game and received five stitches.
"I just tried to be safe, man," Bourn said on Tuesday. "We were down by one and I tried to get on the base. I just tried to get there, but in the process, I got hurt. It's something I have to deal with. That's all I can do."
Francona reiterated on Wednesday that he had no issue with Bourn sliding into first base.
"If every time somebody got hurt, if you told them not to do it, we wouldn't be competing," Francona said. "I told him after he got hurt, I said, 'Bourny, don't change the way you play.' We don't want to lose guys, but that's part of how guys get good. It's not just that. That's just an example of the way he plays. There's other things that you just can't pull back all the time. The guys are competing and they're reacting."
Through 10 games with Cleveland, Bourn was hitting .333 (15-for-45) with two home runs, four doubles, one triple, two RBIs and seven runs scored.
With Bourn sidelined for roughly two weeks, Francona said the Indians will mix and match with the leadoff spot in the batting order. For Wednesday's game against Boston, left fielder Michael Brantley shifted to the top spot in the lineup. Right fielder Drew Stubbs -- the center fielder while Bourn is out -- has also hit leadoff on occasion this season.
Kluber rejoins the Indians as insurance for the club's taxed bullpen. The right-hander will head into the 'pen temporarily after Cleveland's relievers were forced to log 7 1/3 innings in Tuesday's 7-2 loss to Boston. In two starts for Columbus this season, Kluber went 1-1 with a 6.57 ERA. Kluber was called up to Cleveland last week, but he did not pitch in a game due to an April 10 rainout.
Francona said Kluber also offers a contingency plan in the event that lefty Scott Kazmir (right rib cage strain) is unable to come off the 15-day DL as planned for a start on Saturday.
"He's in the bullpen right now," Francona said of Kluber. "Kazmir is going to pitch Saturday, but if for whatever reason something came up, it gives us some protection."