Andriese (hip) threw 37 pitches off the mound at Tropicana Field on Monday, Marc Topkin of the Tampa Bay Times reports.
If he continues without setbacks, Andriese is likely to start a rehab assignment by the end of next week. The 27-year-old right-hander was moved to the 60-day DL back on June 17, but he finally appears to be nearing a return to game action.