Simmons was bidding to join Atlanta's bullpen last week. But after he did not record an out in his second rehab appearance for Triple-A Gwinnett, the rookie reliever was shut down again.
Wren said he did not believe the Braves medical staff believed there was any reason for Simmons to undergo an MRI exam.
"They just think it's a little tender and not quite ready yet, but nothing major," Wren said.
Thoughts of Venters potentially serving as a reliable bullpen piece this year seemed to fade as he spent the past month battling elbow discomfort. But it was not until Tuesday that the Braves essentially ended any lingering hope that Venters might at least experience a feel-good moment by pitching in at least one game this year.
While in Pittsburgh last week, Venters cut one of his bullpen sessions short. After he experienced more elbow discomfort while playing catch in Cincinnati this past weekend, the Braves decided to send him to see Dr. James Andrews, who performed the elbow surgery on Venters in 2005 and again last year.
"Maybe the second time around, it just takes a little longer," Gonzalez said. "I told him to just keep plugging away."
After making 230 appearances -- one shy of the Major League-leading total -- from 2010-2012, Venters underwent his second Tommy John surgery and missed all of the '13 season. Despite understanding the comeback odds that were stacked against Venters, the Braves still took the commendable route by giving the veteran left-handed reliever a one-year, $1.63 million deal that matched his salary from the previous season.
Mark Bowman is a reporter for MLB.com. Teddy Cahill is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.