The right-handed Nunez has been out since May 28 with a strained right lat after an outstanding showing in a setup role for closer Joakim Soria. Nunez had a 1.71 ERA and was 3-1 in 21 games.
"Noonie is a little bit ahead of John," Hillman said. "They're both progressing well. There's a chance of having Noonie back for one, maybe two, games before the All-Star Game, which probably we won't rush.
"He's scheduled for a couple of live batting practice sessions and, if those progress well, a rehab assignment in [Triple-A] Omaha toward the end of next week."
The All-Star Game is on July 15 in the Bronx.
Bale, a left-hander, started the season in the rotation, but was stopped by shoulder fatigue after three starts (0-3, 7.63 ERA) on April 16. While recovering from that, he suffered a broken left hand when he struck a hotel-room door on May 2 in Cleveland, apparently in frustration over a throwing session.
"Johnny is most definitely out until after the All-Star break," Hillman said.
Bale will also have a Minor League rehab assignment when he's ready to pitch.
Dick Kaegel is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.