Manager Ken Macha said before Saturday's game that Hawkins would pitch for Triple-A Nashville again Monday as he continues to rehab from right shoulder weakness.
"We're just going to evaluate his Monday outing," Macha said. "We'll go from there."
Hawkins pitched for the second straight night Friday, tossing 16 pitches over two innings while allowing just one hit as he earned the save.
Macha was hesitant to confirm that Hawkins would rejoin the club after his outing Monday, based on Hawkins' own evaluation of his rehab outings, which Macha received from Brewers trainer Roger Caplinger.
"One of his other outings he kind of indicated he wasn't really on top of his game quite yet," Macha said. "I just got that report from Roger. I didn't talk to [Nashville pitching coach] Rich Gale or anyone like that. Rick Peterson, our pitching coach, will talk to Rich Gale sometime."