Clayton Kershaw threw two simulated innings on Tuesday, but the Los Angeles Dodgers expect him to require a rehab assignment before he can be activated from the disabled list.

"My guess is that Kersh will want to pitch in a Major League game tomorrow," Andrew Friedman said. "With the time he's missed, my guess would be the next step would be a Minor League assignment. I think it will take a little bit of time to build him up in a way for him to be strong through September and hopefully October, as well."

Kershaw has not pitched for the team since June 26 because of a herniated disk in his lower back.

The Dodgers entered Wednesday with a two-game lead over the San Francisco Giants in the National League West.

The Pittsburgh Pirates have placed Gerrit Cole on the disabled list, retroactive to Aug. 25, with "posterior inflammation of the right elbow."

Pittsburgh called up left-hander Steven Brault from Triple-A Indianapolis to assume Cole's spot against the Chicago Cubs on Monday night. He lasted just four innings, striking out four batters and allowed two runs.

The San Francisco Giants have placed Jake Peavy on the 15-day disabled list with a lower back strain.

The move announced Saturday is retroactive to Aug. 21. San Francisco recalled right-hander Albert Suarez from Triple-A Sacramento to start Saturday night's game against the Atlanta Braves in Peavy's place.

Peavy was supposed to start for the first time since a demotion to the bullpen on Aug. 1. 

Bruce Bochy said Peavy "can't pitch the way his back is right now" and that it's "a bad break for him."

The Boston Red Sox have put Andrew Benintendi on the disabled list with a left knee sprain.

Benintendi was injured on Wednesday night against the Tampa Bay Rays while trying to avoid a tag while running toward second base.

John Farrell said team doctors were evaluating the results of an MRI exam on Thursday. The team later said that tests were inconclusive, with more to follow Friday.

The Red Sox are hopeful that the rookie will return before the season ends.

The Baltimore Orioles are placing Chris Tillman on the disabled list with right shoulder inflammation.

Tillman received a cortisone shot on Tuesday.

"I thought once it got loose it would really go away, but it never really did, and that was my first time actually experiencing it while throwing," Tillman said. "Last time, I was pretty sore right after my start, but after feeling it today, I'd much rather just get this behind us and get out in front of it so that way we're not worried about it for the rest of the year."

Ubaldo Jimenez will take Tillman's turn in the rotation on Thursday.

Clayton Kershaw threw a 40-pitch bullpen session Monday at Dodger Stadium and could face live hitters in a simulated game before the end of the week.

Kershaw, who is on the 60-day disabled list with a mild disc herniation in his lower back, said he "felt fine" sitting down between his simulated innings in the bullpen.

"That was the hard part for me before, sitting down in-between innings," he said. "Just not very comfortable to sit. Definitely a positive step there, sitting down, not even thinking about it."

Kershaw is expected to require a Minor League start or two before he is activated off the disabled list.

The Los Angeles Dodgers have tied a Major League record by placing their 27th player on the disabled list this season.

Scott Kazmir went on the DL Tuesday with neck inflammation. Brett Anderson also landed on the DL with a blister on his left index finger, but he had already been on the list this year so he didn't add to the team's total.

The only other team on record to have put 27 players on the DL was the 2012 Boston Red Sox.

The Washington Nationals have placed Stephen Strasburg on the disabled list with right elbow soreness.

Strasburg was willing to pitch through the pain, but the Nationals decided to be cautious.

"I told him we hadn't won anything yet and that we had to look at the big picture," Dusty Baker said. "Hopefully he'll be good in September and hopefully in October."

Strasburg, who is 15-3 with a 3.59 ERA, is expected to spend the minimum amount of time on the DL.

"A hundred percent I think I was good enough to go, but the recovery in between was becoming more of a challenge," he said.

"I felt like I was losing range of motion and wasn't able to get that back in between starts, so I'm trying to make it better than it ever was, I guess. Hopefully that'll translate to some good performance down the road."

The New York Mets have placed Steven Matz on the disabled list with a mild shoulder strain and rotator cuff inflammation.

The move was backdated to August 15.

Matz had been scratched from Friday's start in San Francisco after experiencing shoulder discomfort. The left-hander already has been pitching with a bone spur in his pitching elbow that will need to be surgically removed after the season.

Giancarlo Stanton is aiming to play during the final week of the regular season.

Stanton's season is in jeopardy after he went on the disabled list with a groin strain last week. He suffered a Grade 3 strain and the Miami Marlins put a six-week timeline on the injury.

"I don't think we'll be able to truly assess where he's at until he is doing functional, on-field stuff," Michael Hill said.

Stanton is hitting .244/.329/.496 with 25 home runs in 432 plate appearances this season.