Rodriguez (knee) threw a live batting practice Monday, Scott Lauber of ESPN.com reports.
Rodriguez will throw another session on Wednesday and could pitch in a minor league rehab start early next week. The 22-year-old had a 3.85 ERA over 21 starts for the Red Sox in 2015 and is expected to be a key part of their rotation once he returns from injury. The Red Sox have said they hope to have Rodriguez back in late April or early May.