Holland was looking at a return in mid-July, but Daniels said that might be pushed to late July or early August.
"I think Derek wants us to push it, but we're not going to do that," Daniels said.
Holland underwent an MRI on Friday that revealed "continued progress" in his rehab. Daniels said he hasn't seen the MRI results, but he said reports indicate Holland's shoulder inflammation is about 90 percent healed.
Holland threw from 90 feet for the first time in his rehab Monday, and he will do the same Wednesday and Friday. He has not yet been cleared to throw off a mound and has another MRI scheduled for June 19.
"He hasn't had any setback or anything like that," Daniels said. "I think after our experience with Jurickson, I think we want to be extremely cautious here and make sure he's got a totally clean MRI, a 100 percent clean scan.
"[His return] still could be [mid-July], but it also could be a couple weeks afterward."
Matt Harrison took a loss and allowed eight hits and six earned runs over five innings Monday against the Oklahoma City Dodgers in his second Triple-A rehab start for Round Rock.
Harrison hasn't pitched in the Majors since May 13, 2014, and later underwent lower lumbar spinal fusion surgery June 3, 2014.
"I feel like this is the best stuff I've had come out of my hand since I've been getting off the mound in these games," Harrison said. "I've just been having a little bit of timing issues with the mechanics. I tried something different between my last start, get my legs more involved on the delivery and the ball is definitely coming out better."
Harrison went five innings and allowed five hits and two earned runs in his first rehab start.
He has a 49-33 career record with a 4.15 ERA. In 2012, Harrison went 18-11 with a 3.39 ERA for the Rangers.
Cody Stavenhagen is an associate reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.