"I feel good," Zambrano said. "I'm ready to keep doing my exercises and see what is scheduled for me."
Sunday will be his first bullpen session since his last start June 18 against Tampa Bay, which he left after 6 2/3 innings because of discomfort.
"One thing I learned from this was it's good when you work harder than normal," Zambrano said. "You never give up -- you should keep working, working, working. Sometimes you come and you're lazy and you don't want to do nothing, but that's the day you have to do more. My arm will appreciate anything I can do to keep up my arm strength."
The right-hander, who is 8-3 with a 3.13 ERA, ranks among the NL leaders in ERA and innings pitched. He was projected to miss two starts and would be eligible to come off the DL during the Cubs' series in St. Louis July 4-6.
He could be one of the pitchers chosen for the All-Star Game, along with teammate Ryan Dempster.
"I want to pitch in the All-Star Game," Zambrano said. "I want to help the National League, so if we are in the World Series, we can have [home-field] advantage. A little help from me or [Brandon] Webb or [Edinson] Volquez, we can finally win one after four, five years."
Fukudome, who was scratched from Wednesday's game because of tightness in his left calf, ran in the outfield Thursday to test his leg.
"I didn't go full speed, so I couldn't really tell," Fukudome said through interpreter Ryuji Araki.
The pain is believed to be related to playing on artificial turf in Toronto and Tampa Bay for six straight games. He was available to pinch-hit Thursday, and may be back in the lineup this weekend for the Cubs' Interleague series against the White Sox.
Carrie Muskat is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.