On Saturday, Gonzalez threw off the mound for the first time and, assuming he comes out of Monday's session OK, he will throw an inning in an extended spring camp game on Thursday.
Gonzalez has been working his way back from a left-shoulder strain that he has said previously started to plague him in the days leading up to April 10, which was his final appearance before being placed on the DL April 15.
Orioles manager Dave Trembley said that there are no plans for Gonzalez beyond Thursday. But given Gonzalez's progression, early June would be a likely target date so long as he experiences no setbacks.
A lefty with a herky-jerky delivery, Gonzalez appeared in three games for the Orioles, pitching to an 0-2 record and an 18.00 ERA, before being put on the shelf. In his absence, the Orioles have relied heavily on Alfredo Simon, who has become the team's de facto closer. A power pitcher, Simon was charged with his first loss and blown save of the season in Saturday's 8-2 loss, surrendering four runs on three hits and recording just one out in the ninth inning.
Trembley said Simon was available if needed on Sunday and chose to not speculate further down the road.
"I believe that's the proper way to go about it," he said. "I can't guarantee that he will close for the next 10 times in a row."