Manager Ryne Sandberg indicated Lee could begin a Minor League rehab assignment next week.
"Possibly, if all goes well, that would be the next step," Sandberg said before Wednesday's game against the Marlins.
Lee has not ruled out returning before the All-Star break. If not, he's likely to be ready for the first series after the break on July 18-20 in Atlanta.
Austin Laymance is a reporter for MLB.com. Follow him on Twitter at @jalaymance. Todd Zolecki is a reporter for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.