Odorizzi (hamstring) is scheduled to throw four innings in a simulated game Tuesday, Marc Topkin of the Tampa Bay Times reports.
Odorizzi is nearing a return to the Rays after tossing a 36-pitch bullpen Saturday without any issues. He'll get up and down four times in his next session to simulate a game, and if all goes well, it's looking like he could return to the lineup for next Monday's matchup against the Marlins.