Nunez (shoulder) was cleared Saturday to begin a rehab assignment in the Florida Complex League, Jason Mackey of the Pittsburgh Post-Gazette reports.
If all goes well, he should be able to return from the injured list at Triple-A Indianapolis before the end of July. The 22-year-old had caught fire just prior to injuring his right shoulder in May, but he carries an underwhelming .260/.351/.377 overall batting line in 160 plate appearances this season in the International League.